{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.1, 3.5, 1.4, 0.2],\n",
       "       [4.9, 3. , 1.4, 0.2],\n",
       "       [4.7, 3.2, 1.3, 0.2],\n",
       "       [4.6, 3.1, 1.5, 0.2],\n",
       "       [5. , 3.6, 1.4, 0.2],\n",
       "       [5.4, 3.9, 1.7, 0.4],\n",
       "       [4.6, 3.4, 1.4, 0.3],\n",
       "       [5. , 3.4, 1.5, 0.2],\n",
       "       [4.4, 2.9, 1.4, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [5.4, 3.7, 1.5, 0.2],\n",
       "       [4.8, 3.4, 1.6, 0.2],\n",
       "       [4.8, 3. , 1.4, 0.1],\n",
       "       [4.3, 3. , 1.1, 0.1],\n",
       "       [5.8, 4. , 1.2, 0.2],\n",
       "       [5.7, 4.4, 1.5, 0.4],\n",
       "       [5.4, 3.9, 1.3, 0.4],\n",
       "       [5.1, 3.5, 1.4, 0.3],\n",
       "       [5.7, 3.8, 1.7, 0.3],\n",
       "       [5.1, 3.8, 1.5, 0.3],\n",
       "       [5.4, 3.4, 1.7, 0.2],\n",
       "       [5.1, 3.7, 1.5, 0.4],\n",
       "       [4.6, 3.6, 1. , 0.2],\n",
       "       [5.1, 3.3, 1.7, 0.5],\n",
       "       [4.8, 3.4, 1.9, 0.2],\n",
       "       [5. , 3. , 1.6, 0.2],\n",
       "       [5. , 3.4, 1.6, 0.4],\n",
       "       [5.2, 3.5, 1.5, 0.2],\n",
       "       [5.2, 3.4, 1.4, 0.2],\n",
       "       [4.7, 3.2, 1.6, 0.2],\n",
       "       [4.8, 3.1, 1.6, 0.2],\n",
       "       [5.4, 3.4, 1.5, 0.4],\n",
       "       [5.2, 4.1, 1.5, 0.1],\n",
       "       [5.5, 4.2, 1.4, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.2],\n",
       "       [5. , 3.2, 1.2, 0.2],\n",
       "       [5.5, 3.5, 1.3, 0.2],\n",
       "       [4.9, 3.6, 1.4, 0.1],\n",
       "       [4.4, 3. , 1.3, 0.2],\n",
       "       [5.1, 3.4, 1.5, 0.2],\n",
       "       [5. , 3.5, 1.3, 0.3],\n",
       "       [4.5, 2.3, 1.3, 0.3],\n",
       "       [4.4, 3.2, 1.3, 0.2],\n",
       "       [5. , 3.5, 1.6, 0.6],\n",
       "       [5.1, 3.8, 1.9, 0.4],\n",
       "       [4.8, 3. , 1.4, 0.3],\n",
       "       [5.1, 3.8, 1.6, 0.2],\n",
       "       [4.6, 3.2, 1.4, 0.2],\n",
       "       [5.3, 3.7, 1.5, 0.2],\n",
       "       [5. , 3.3, 1.4, 0.2],\n",
       "       [7. , 3.2, 4.7, 1.4],\n",
       "       [6.4, 3.2, 4.5, 1.5],\n",
       "       [6.9, 3.1, 4.9, 1.5],\n",
       "       [5.5, 2.3, 4. , 1.3],\n",
       "       [6.5, 2.8, 4.6, 1.5],\n",
       "       [5.7, 2.8, 4.5, 1.3],\n",
       "       [6.3, 3.3, 4.7, 1.6],\n",
       "       [4.9, 2.4, 3.3, 1. ],\n",
       "       [6.6, 2.9, 4.6, 1.3],\n",
       "       [5.2, 2.7, 3.9, 1.4],\n",
       "       [5. , 2. , 3.5, 1. ],\n",
       "       [5.9, 3. , 4.2, 1.5],\n",
       "       [6. , 2.2, 4. , 1. ],\n",
       "       [6.1, 2.9, 4.7, 1.4],\n",
       "       [5.6, 2.9, 3.6, 1.3],\n",
       "       [6.7, 3.1, 4.4, 1.4],\n",
       "       [5.6, 3. , 4.5, 1.5],\n",
       "       [5.8, 2.7, 4.1, 1. ],\n",
       "       [6.2, 2.2, 4.5, 1.5],\n",
       "       [5.6, 2.5, 3.9, 1.1],\n",
       "       [5.9, 3.2, 4.8, 1.8],\n",
       "       [6.1, 2.8, 4. , 1.3],\n",
       "       [6.3, 2.5, 4.9, 1.5],\n",
       "       [6.1, 2.8, 4.7, 1.2],\n",
       "       [6.4, 2.9, 4.3, 1.3],\n",
       "       [6.6, 3. , 4.4, 1.4],\n",
       "       [6.8, 2.8, 4.8, 1.4],\n",
       "       [6.7, 3. , 5. , 1.7],\n",
       "       [6. , 2.9, 4.5, 1.5],\n",
       "       [5.7, 2.6, 3.5, 1. ],\n",
       "       [5.5, 2.4, 3.8, 1.1],\n",
       "       [5.5, 2.4, 3.7, 1. ],\n",
       "       [5.8, 2.7, 3.9, 1.2],\n",
       "       [6. , 2.7, 5.1, 1.6],\n",
       "       [5.4, 3. , 4.5, 1.5],\n",
       "       [6. , 3.4, 4.5, 1.6],\n",
       "       [6.7, 3.1, 4.7, 1.5],\n",
       "       [6.3, 2.3, 4.4, 1.3],\n",
       "       [5.6, 3. , 4.1, 1.3],\n",
       "       [5.5, 2.5, 4. , 1.3],\n",
       "       [5.5, 2.6, 4.4, 1.2],\n",
       "       [6.1, 3. , 4.6, 1.4],\n",
       "       [5.8, 2.6, 4. , 1.2],\n",
       "       [5. , 2.3, 3.3, 1. ],\n",
       "       [5.6, 2.7, 4.2, 1.3],\n",
       "       [5.7, 3. , 4.2, 1.2],\n",
       "       [5.7, 2.9, 4.2, 1.3],\n",
       "       [6.2, 2.9, 4.3, 1.3],\n",
       "       [5.1, 2.5, 3. , 1.1],\n",
       "       [5.7, 2.8, 4.1, 1.3],\n",
       "       [6.3, 3.3, 6. , 2.5],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [7.1, 3. , 5.9, 2.1],\n",
       "       [6.3, 2.9, 5.6, 1.8],\n",
       "       [6.5, 3. , 5.8, 2.2],\n",
       "       [7.6, 3. , 6.6, 2.1],\n",
       "       [4.9, 2.5, 4.5, 1.7],\n",
       "       [7.3, 2.9, 6.3, 1.8],\n",
       "       [6.7, 2.5, 5.8, 1.8],\n",
       "       [7.2, 3.6, 6.1, 2.5],\n",
       "       [6.5, 3.2, 5.1, 2. ],\n",
       "       [6.4, 2.7, 5.3, 1.9],\n",
       "       [6.8, 3. , 5.5, 2.1],\n",
       "       [5.7, 2.5, 5. , 2. ],\n",
       "       [5.8, 2.8, 5.1, 2.4],\n",
       "       [6.4, 3.2, 5.3, 2.3],\n",
       "       [6.5, 3. , 5.5, 1.8],\n",
       "       [7.7, 3.8, 6.7, 2.2],\n",
       "       [7.7, 2.6, 6.9, 2.3],\n",
       "       [6. , 2.2, 5. , 1.5],\n",
       "       [6.9, 3.2, 5.7, 2.3],\n",
       "       [5.6, 2.8, 4.9, 2. ],\n",
       "       [7.7, 2.8, 6.7, 2. ],\n",
       "       [6.3, 2.7, 4.9, 1.8],\n",
       "       [6.7, 3.3, 5.7, 2.1],\n",
       "       [7.2, 3.2, 6. , 1.8],\n",
       "       [6.2, 2.8, 4.8, 1.8],\n",
       "       [6.1, 3. , 4.9, 1.8],\n",
       "       [6.4, 2.8, 5.6, 2.1],\n",
       "       [7.2, 3. , 5.8, 1.6],\n",
       "       [7.4, 2.8, 6.1, 1.9],\n",
       "       [7.9, 3.8, 6.4, 2. ],\n",
       "       [6.4, 2.8, 5.6, 2.2],\n",
       "       [6.3, 2.8, 5.1, 1.5],\n",
       "       [6.1, 2.6, 5.6, 1.4],\n",
       "       [7.7, 3. , 6.1, 2.3],\n",
       "       [6.3, 3.4, 5.6, 2.4],\n",
       "       [6.4, 3.1, 5.5, 1.8],\n",
       "       [6. , 3. , 4.8, 1.8],\n",
       "       [6.9, 3.1, 5.4, 2.1],\n",
       "       [6.7, 3.1, 5.6, 2.4],\n",
       "       [6.9, 3.1, 5.1, 2.3],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [6.8, 3.2, 5.9, 2.3],\n",
       "       [6.7, 3.3, 5.7, 2.5],\n",
       "       [6.7, 3. , 5.2, 2.3],\n",
       "       [6.3, 2.5, 5. , 1.9],\n",
       "       [6.5, 3. , 5.2, 2. ],\n",
       "       [6.2, 3.4, 5.4, 2.3],\n",
       "       [5.9, 3. , 5.1, 1.8]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = iris.data\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = iris.target\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 4)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       0    1    2    3\n",
       "0    5.1  3.5  1.4  0.2\n",
       "1    4.9  3.0  1.4  0.2\n",
       "2    4.7  3.2  1.3  0.2\n",
       "3    4.6  3.1  1.5  0.2\n",
       "4    5.0  3.6  1.4  0.2\n",
       "..   ...  ...  ...  ...\n",
       "145  6.7  3.0  5.2  2.3\n",
       "146  6.3  2.5  5.0  1.9\n",
       "147  6.5  3.0  5.2  2.0\n",
       "148  6.2  3.4  5.4  2.3\n",
       "149  5.9  3.0  5.1  1.8\n",
       "\n",
       "[150 rows x 4 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 建模调用PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.68412563,  0.31939725],\n",
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       "       [ 1.55780216,  0.26749545],\n",
       "       [ 0.81329065, -0.1633503 ],\n",
       "       [-0.30558378, -0.36826219],\n",
       "       [-0.06812649, -0.70517213],\n",
       "       [-0.18962247, -0.68028676],\n",
       "       [ 0.13642871, -0.31403244],\n",
       "       [ 1.38002644, -0.42095429],\n",
       "       [ 0.58800644, -0.48428742],\n",
       "       [ 0.80685831,  0.19418231],\n",
       "       [ 1.22069088,  0.40761959],\n",
       "       [ 0.81509524, -0.37203706],\n",
       "       [ 0.24595768, -0.2685244 ],\n",
       "       [ 0.16641322, -0.68192672],\n",
       "       [ 0.46480029, -0.67071154],\n",
       "       [ 0.8908152 , -0.03446444],\n",
       "       [ 0.23054802, -0.40438585],\n",
       "       [-0.70453176, -1.01224823],\n",
       "       [ 0.35698149, -0.50491009],\n",
       "       [ 0.33193448, -0.21265468],\n",
       "       [ 0.37621565, -0.29321893],\n",
       "       [ 0.64257601,  0.01773819],\n",
       "       [-0.90646986, -0.75609337],\n",
       "       [ 0.29900084, -0.34889781],\n",
       "       [ 2.53119273, -0.00984911],\n",
       "       [ 1.41523588, -0.57491635],\n",
       "       [ 2.61667602,  0.34390315],\n",
       "       [ 1.97153105, -0.1797279 ],\n",
       "       [ 2.35000592, -0.04026095],\n",
       "       [ 3.39703874,  0.55083667],\n",
       "       [ 0.52123224, -1.19275873],\n",
       "       [ 2.93258707,  0.3555    ],\n",
       "       [ 2.32122882, -0.2438315 ],\n",
       "       [ 2.91675097,  0.78279195],\n",
       "       [ 1.66177415,  0.24222841],\n",
       "       [ 1.80340195, -0.21563762],\n",
       "       [ 2.1655918 ,  0.21627559],\n",
       "       [ 1.34616358, -0.77681835],\n",
       "       [ 1.58592822, -0.53964071],\n",
       "       [ 1.90445637,  0.11925069],\n",
       "       [ 1.94968906,  0.04194326],\n",
       "       [ 3.48705536,  1.17573933],\n",
       "       [ 3.79564542,  0.25732297],\n",
       "       [ 1.30079171, -0.76114964],\n",
       "       [ 2.42781791,  0.37819601],\n",
       "       [ 1.19900111, -0.60609153],\n",
       "       [ 3.49992004,  0.4606741 ],\n",
       "       [ 1.38876613, -0.20439933],\n",
       "       [ 2.2754305 ,  0.33499061],\n",
       "       [ 2.61409047,  0.56090136],\n",
       "       [ 1.25850816, -0.17970479],\n",
       "       [ 1.29113206, -0.11666865],\n",
       "       [ 2.12360872, -0.20972948],\n",
       "       [ 2.38800302,  0.4646398 ],\n",
       "       [ 2.84167278,  0.37526917],\n",
       "       [ 3.23067366,  1.37416509],\n",
       "       [ 2.15943764, -0.21727758],\n",
       "       [ 1.44416124, -0.14341341],\n",
       "       [ 1.78129481, -0.49990168],\n",
       "       [ 3.07649993,  0.68808568],\n",
       "       [ 2.14424331,  0.1400642 ],\n",
       "       [ 1.90509815,  0.04930053],\n",
       "       [ 1.16932634, -0.16499026],\n",
       "       [ 2.10761114,  0.37228787],\n",
       "       [ 2.31415471,  0.18365128],\n",
       "       [ 1.9222678 ,  0.40920347],\n",
       "       [ 1.41523588, -0.57491635],\n",
       "       [ 2.56301338,  0.2778626 ],\n",
       "       [ 2.41874618,  0.3047982 ],\n",
       "       [ 1.94410979,  0.1875323 ],\n",
       "       [ 1.52716661, -0.37531698],\n",
       "       [ 1.76434572,  0.07885885],\n",
       "       [ 1.90094161,  0.11662796],\n",
       "       [ 1.39018886, -0.28266094]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=2)\n",
    "pca = pca.fit(x)\n",
    "x_dr = pca.transform(x)\n",
    "x_dr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = ['red', 'black', 'orange']\n",
    "\n",
    "plt.figure()\n",
    "for i in [0,1,2]:\n",
    "    plt.scatter(x_dr[y==i, 0], x_dr[y==i, 1],\n",
    "               alpha=.7,\n",
    "               c=colors[i],\n",
    "               label=iris.target_names[i])\n",
    "plt.legend()\n",
    "plt.title('iris data')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数据探索"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.22824171, 0.24267075])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.977685206318795"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.92461872, 0.05306648])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 选择最好的n_components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca_line = PCA().fit(x)\n",
    "plt.plot([1,2,3,4], np.cumsum(pca_line.explained_variance_ratio_))\n",
    "plt.xticks([1,2,3,4])\n",
    "plt.xlabel(\"number of components after dimension reduction\")\n",
    "plt.ylabel(\"cumulative explained variance ratio\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 最大似然估计自选超参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.68412563,  0.31939725, -0.02791483],\n",
       "       [-2.71414169, -0.17700123, -0.21046427],\n",
       "       [-2.88899057, -0.14494943,  0.01790026],\n",
       "       [-2.74534286, -0.31829898,  0.03155937],\n",
       "       [-2.72871654,  0.32675451,  0.09007924],\n",
       "       [-2.28085963,  0.74133045,  0.16867766],\n",
       "       [-2.82053775, -0.08946138,  0.25789216],\n",
       "       [-2.62614497,  0.16338496, -0.02187932],\n",
       "       [-2.88638273, -0.57831175,  0.02075957],\n",
       "       [-2.6727558 , -0.11377425, -0.19763272],\n",
       "       [-2.50694709,  0.6450689 , -0.07531801],\n",
       "       [-2.61275523,  0.01472994,  0.10215026],\n",
       "       [-2.78610927, -0.235112  , -0.20684443],\n",
       "       [-3.22380374, -0.51139459,  0.06129967],\n",
       "       [-2.64475039,  1.17876464, -0.15162752],\n",
       "       [-2.38603903,  1.33806233,  0.2777769 ],\n",
       "       [-2.62352788,  0.81067951,  0.13818323],\n",
       "       [-2.64829671,  0.31184914,  0.02666832],\n",
       "       [-2.19982032,  0.87283904, -0.12030552],\n",
       "       [-2.5879864 ,  0.51356031,  0.21366517],\n",
       "       [-2.31025622,  0.39134594, -0.23944404],\n",
       "       [-2.54370523,  0.43299606,  0.20845723],\n",
       "       [-3.21593942,  0.13346807,  0.29239675],\n",
       "       [-2.30273318,  0.09870885,  0.03912326],\n",
       "       [-2.35575405, -0.03728186,  0.12502108],\n",
       "       [-2.50666891, -0.14601688, -0.25342004],\n",
       "       [-2.46882007,  0.13095149,  0.09491058],\n",
       "       [-2.56231991,  0.36771886, -0.07849421],\n",
       "       [-2.63953472,  0.31203998, -0.1459089 ],\n",
       "       [-2.63198939, -0.19696122,  0.04077108],\n",
       "       [-2.58739848, -0.20431849, -0.07722299],\n",
       "       [-2.4099325 ,  0.41092426, -0.14552497],\n",
       "       [-2.64886233,  0.81336382,  0.22566915],\n",
       "       [-2.59873675,  1.09314576,  0.15781081],\n",
       "       [-2.63692688, -0.12132235, -0.14304958],\n",
       "       [-2.86624165,  0.06936447, -0.16433231],\n",
       "       [-2.62523805,  0.59937002, -0.26835038],\n",
       "       [-2.80068412,  0.26864374,  0.09369908],\n",
       "       [-2.98050204, -0.48795834,  0.07292705],\n",
       "       [-2.59000631,  0.22904384, -0.0800823 ],\n",
       "       [-2.77010243,  0.26352753,  0.07724769],\n",
       "       [-2.84936871, -0.94096057, -0.34923038],\n",
       "       [-2.99740655, -0.34192606,  0.19250921],\n",
       "       [-2.40561449,  0.18887143,  0.26386795],\n",
       "       [-2.20948924,  0.43666314,  0.29874275],\n",
       "       [-2.71445143, -0.2502082 , -0.09767814],\n",
       "       [-2.53814826,  0.50377114,  0.16670564],\n",
       "       [-2.83946217, -0.22794557,  0.08372685],\n",
       "       [-2.54308575,  0.57941002, -0.01711502],\n",
       "       [-2.70335978,  0.10770608, -0.08929401],\n",
       "       [ 1.28482569,  0.68516047, -0.40656803],\n",
       "       [ 0.93248853,  0.31833364, -0.01801419],\n",
       "       [ 1.46430232,  0.50426282, -0.33832576],\n",
       "       [ 0.18331772, -0.82795901, -0.17959139],\n",
       "       [ 1.08810326,  0.07459068, -0.3077579 ],\n",
       "       [ 0.64166908, -0.41824687,  0.04107609],\n",
       "       [ 1.09506066,  0.28346827,  0.16981024],\n",
       "       [-0.74912267, -1.00489096,  0.01230292],\n",
       "       [ 1.04413183,  0.2283619 , -0.41533608],\n",
       "       [-0.0087454 , -0.72308191,  0.28114143],\n",
       "       [-0.50784088, -1.26597119, -0.26981718],\n",
       "       [ 0.51169856, -0.10398124,  0.13054775],\n",
       "       [ 0.26497651, -0.55003646, -0.69414683],\n",
       "       [ 0.98493451, -0.12481785, -0.06211441],\n",
       "       [-0.17392537, -0.25485421,  0.09045769],\n",
       "       [ 0.92786078,  0.46717949, -0.31462098],\n",
       "       [ 0.66028376, -0.35296967,  0.32802753],\n",
       "       [ 0.23610499, -0.33361077, -0.27116184],\n",
       "       [ 0.94473373, -0.54314555, -0.49951905],\n",
       "       [ 0.04522698, -0.58383438, -0.2350021 ],\n",
       "       [ 1.11628318, -0.08461685,  0.45962099],\n",
       "       [ 0.35788842, -0.06892503, -0.22985389],\n",
       "       [ 1.29818388, -0.32778731, -0.34785435],\n",
       "       [ 0.92172892, -0.18273779, -0.23107178],\n",
       "       [ 0.71485333,  0.14905594, -0.32180094],\n",
       "       [ 0.90017437,  0.32850447, -0.31620907],\n",
       "       [ 1.33202444,  0.24444088, -0.52170278],\n",
       "       [ 1.55780216,  0.26749545, -0.16492098],\n",
       "       [ 0.81329065, -0.1633503 ,  0.0354245 ],\n",
       "       [-0.30558378, -0.36826219, -0.31849158],\n",
       "       [-0.06812649, -0.70517213, -0.24421381],\n",
       "       [-0.18962247, -0.68028676, -0.30642056],\n",
       "       [ 0.13642871, -0.31403244, -0.17724277],\n",
       "       [ 1.38002644, -0.42095429,  0.01616713],\n",
       "       [ 0.58800644, -0.48428742,  0.4444335 ],\n",
       "       [ 0.80685831,  0.19418231,  0.38896306],\n",
       "       [ 1.22069088,  0.40761959, -0.23716701],\n",
       "       [ 0.81509524, -0.37203706, -0.61472084],\n",
       "       [ 0.24595768, -0.2685244 ,  0.18836681],\n",
       "       [ 0.16641322, -0.68192672, -0.06000923],\n",
       "       [ 0.46480029, -0.67071154, -0.02430686],\n",
       "       [ 0.8908152 , -0.03446444, -0.00994693],\n",
       "       [ 0.23054802, -0.40438585, -0.22941024],\n",
       "       [-0.70453176, -1.01224823, -0.10569115],\n",
       "       [ 0.35698149, -0.50491009,  0.01661717],\n",
       "       [ 0.33193448, -0.21265468,  0.08320429],\n",
       "       [ 0.37621565, -0.29321893,  0.07799635],\n",
       "       [ 0.64257601,  0.01773819, -0.20539497],\n",
       "       [-0.90646986, -0.75609337, -0.01259965],\n",
       "       [ 0.29900084, -0.34889781,  0.01058166],\n",
       "       [ 2.53119273, -0.00984911,  0.76016543],\n",
       "       [ 1.41523588, -0.57491635,  0.29632253],\n",
       "       [ 2.61667602,  0.34390315, -0.11078788],\n",
       "       [ 1.97153105, -0.1797279 ,  0.10842466],\n",
       "       [ 2.35000592, -0.04026095,  0.28538956],\n",
       "       [ 3.39703874,  0.55083667, -0.34843756],\n",
       "       [ 0.52123224, -1.19275873,  0.5456593 ],\n",
       "       [ 2.93258707,  0.3555    , -0.42023994],\n",
       "       [ 2.32122882, -0.2438315 , -0.34830439],\n",
       "       [ 2.91675097,  0.78279195,  0.42333542],\n",
       "       [ 1.66177415,  0.24222841,  0.24244019],\n",
       "       [ 1.80340195, -0.21563762, -0.03764817],\n",
       "       [ 2.1655918 ,  0.21627559,  0.03332664],\n",
       "       [ 1.34616358, -0.77681835,  0.28190288],\n",
       "       [ 1.58592822, -0.53964071,  0.62902933],\n",
       "       [ 1.90445637,  0.11925069,  0.47963982],\n",
       "       [ 1.94968906,  0.04194326,  0.04418617],\n",
       "       [ 3.48705536,  1.17573933,  0.13389487],\n",
       "       [ 3.79564542,  0.25732297, -0.51376776],\n",
       "       [ 1.30079171, -0.76114964, -0.34499504],\n",
       "       [ 2.42781791,  0.37819601,  0.21911932],\n",
       "       [ 1.19900111, -0.60609153,  0.51185551],\n",
       "       [ 3.49992004,  0.4606741 , -0.57318224],\n",
       "       [ 1.38876613, -0.20439933, -0.06452276],\n",
       "       [ 2.2754305 ,  0.33499061,  0.28615009],\n",
       "       [ 2.61409047,  0.56090136, -0.20553452],\n",
       "       [ 1.25850816, -0.17970479,  0.0458477 ],\n",
       "       [ 1.29113206, -0.11666865,  0.23125646],\n",
       "       [ 2.12360872, -0.20972948,  0.15418002],\n",
       "       [ 2.38800302,  0.4646398 , -0.44953019],\n",
       "       [ 2.84167278,  0.37526917, -0.49889808],\n",
       "       [ 3.23067366,  1.37416509, -0.11454821],\n",
       "       [ 2.15943764, -0.21727758,  0.20876317],\n",
       "       [ 1.44416124, -0.14341341, -0.15323389],\n",
       "       [ 1.78129481, -0.49990168, -0.17287519],\n",
       "       [ 3.07649993,  0.68808568, -0.33559229],\n",
       "       [ 2.14424331,  0.1400642 ,  0.73487894],\n",
       "       [ 1.90509815,  0.04930053,  0.16218024],\n",
       "       [ 1.16932634, -0.16499026,  0.28183584],\n",
       "       [ 2.10761114,  0.37228787,  0.02729113],\n",
       "       [ 2.31415471,  0.18365128,  0.32269375],\n",
       "       [ 1.9222678 ,  0.40920347,  0.1135866 ],\n",
       "       [ 1.41523588, -0.57491635,  0.29632253],\n",
       "       [ 2.56301338,  0.2778626 ,  0.29256952],\n",
       "       [ 2.41874618,  0.3047982 ,  0.50448266],\n",
       "       [ 1.94410979,  0.1875323 ,  0.17782509],\n",
       "       [ 1.52716661, -0.37531698, -0.12189817],\n",
       "       [ 1.76434572,  0.07885885,  0.13048163],\n",
       "       [ 1.90094161,  0.11662796,  0.72325156],\n",
       "       [ 1.39018886, -0.28266094,  0.36290965]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_mle = PCA(n_components=\"mle\")\n",
    "pla_mle = pca_mle.fit(x)\n",
    "x_mle = pca_mle.transform(x)\n",
    "\n",
    "x_mle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.92461872, 0.05306648, 0.01710261])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_mle.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.977685206318795"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 按信息量占比选超参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.68412563,  0.31939725],\n",
       "       [-2.71414169, -0.17700123],\n",
       "       [-2.88899057, -0.14494943],\n",
       "       [-2.74534286, -0.31829898],\n",
       "       [-2.72871654,  0.32675451],\n",
       "       [-2.28085963,  0.74133045],\n",
       "       [-2.82053775, -0.08946138],\n",
       "       [-2.62614497,  0.16338496],\n",
       "       [-2.88638273, -0.57831175],\n",
       "       [-2.6727558 , -0.11377425],\n",
       "       [-2.50694709,  0.6450689 ],\n",
       "       [-2.61275523,  0.01472994],\n",
       "       [-2.78610927, -0.235112  ],\n",
       "       [-3.22380374, -0.51139459],\n",
       "       [-2.64475039,  1.17876464],\n",
       "       [-2.38603903,  1.33806233],\n",
       "       [-2.62352788,  0.81067951],\n",
       "       [-2.64829671,  0.31184914],\n",
       "       [-2.19982032,  0.87283904],\n",
       "       [-2.5879864 ,  0.51356031],\n",
       "       [-2.31025622,  0.39134594],\n",
       "       [-2.54370523,  0.43299606],\n",
       "       [-3.21593942,  0.13346807],\n",
       "       [-2.30273318,  0.09870885],\n",
       "       [-2.35575405, -0.03728186],\n",
       "       [-2.50666891, -0.14601688],\n",
       "       [-2.46882007,  0.13095149],\n",
       "       [-2.56231991,  0.36771886],\n",
       "       [-2.63953472,  0.31203998],\n",
       "       [-2.63198939, -0.19696122],\n",
       "       [-2.58739848, -0.20431849],\n",
       "       [-2.4099325 ,  0.41092426],\n",
       "       [-2.64886233,  0.81336382],\n",
       "       [-2.59873675,  1.09314576],\n",
       "       [-2.63692688, -0.12132235],\n",
       "       [-2.86624165,  0.06936447],\n",
       "       [-2.62523805,  0.59937002],\n",
       "       [-2.80068412,  0.26864374],\n",
       "       [-2.98050204, -0.48795834],\n",
       "       [-2.59000631,  0.22904384],\n",
       "       [-2.77010243,  0.26352753],\n",
       "       [-2.84936871, -0.94096057],\n",
       "       [-2.99740655, -0.34192606],\n",
       "       [-2.40561449,  0.18887143],\n",
       "       [-2.20948924,  0.43666314],\n",
       "       [-2.71445143, -0.2502082 ],\n",
       "       [-2.53814826,  0.50377114],\n",
       "       [-2.83946217, -0.22794557],\n",
       "       [-2.54308575,  0.57941002],\n",
       "       [-2.70335978,  0.10770608],\n",
       "       [ 1.28482569,  0.68516047],\n",
       "       [ 0.93248853,  0.31833364],\n",
       "       [ 1.46430232,  0.50426282],\n",
       "       [ 0.18331772, -0.82795901],\n",
       "       [ 1.08810326,  0.07459068],\n",
       "       [ 0.64166908, -0.41824687],\n",
       "       [ 1.09506066,  0.28346827],\n",
       "       [-0.74912267, -1.00489096],\n",
       "       [ 1.04413183,  0.2283619 ],\n",
       "       [-0.0087454 , -0.72308191],\n",
       "       [-0.50784088, -1.26597119],\n",
       "       [ 0.51169856, -0.10398124],\n",
       "       [ 0.26497651, -0.55003646],\n",
       "       [ 0.98493451, -0.12481785],\n",
       "       [-0.17392537, -0.25485421],\n",
       "       [ 0.92786078,  0.46717949],\n",
       "       [ 0.66028376, -0.35296967],\n",
       "       [ 0.23610499, -0.33361077],\n",
       "       [ 0.94473373, -0.54314555],\n",
       "       [ 0.04522698, -0.58383438],\n",
       "       [ 1.11628318, -0.08461685],\n",
       "       [ 0.35788842, -0.06892503],\n",
       "       [ 1.29818388, -0.32778731],\n",
       "       [ 0.92172892, -0.18273779],\n",
       "       [ 0.71485333,  0.14905594],\n",
       "       [ 0.90017437,  0.32850447],\n",
       "       [ 1.33202444,  0.24444088],\n",
       "       [ 1.55780216,  0.26749545],\n",
       "       [ 0.81329065, -0.1633503 ],\n",
       "       [-0.30558378, -0.36826219],\n",
       "       [-0.06812649, -0.70517213],\n",
       "       [-0.18962247, -0.68028676],\n",
       "       [ 0.13642871, -0.31403244],\n",
       "       [ 1.38002644, -0.42095429],\n",
       "       [ 0.58800644, -0.48428742],\n",
       "       [ 0.80685831,  0.19418231],\n",
       "       [ 1.22069088,  0.40761959],\n",
       "       [ 0.81509524, -0.37203706],\n",
       "       [ 0.24595768, -0.2685244 ],\n",
       "       [ 0.16641322, -0.68192672],\n",
       "       [ 0.46480029, -0.67071154],\n",
       "       [ 0.8908152 , -0.03446444],\n",
       "       [ 0.23054802, -0.40438585],\n",
       "       [-0.70453176, -1.01224823],\n",
       "       [ 0.35698149, -0.50491009],\n",
       "       [ 0.33193448, -0.21265468],\n",
       "       [ 0.37621565, -0.29321893],\n",
       "       [ 0.64257601,  0.01773819],\n",
       "       [-0.90646986, -0.75609337],\n",
       "       [ 0.29900084, -0.34889781],\n",
       "       [ 2.53119273, -0.00984911],\n",
       "       [ 1.41523588, -0.57491635],\n",
       "       [ 2.61667602,  0.34390315],\n",
       "       [ 1.97153105, -0.1797279 ],\n",
       "       [ 2.35000592, -0.04026095],\n",
       "       [ 3.39703874,  0.55083667],\n",
       "       [ 0.52123224, -1.19275873],\n",
       "       [ 2.93258707,  0.3555    ],\n",
       "       [ 2.32122882, -0.2438315 ],\n",
       "       [ 2.91675097,  0.78279195],\n",
       "       [ 1.66177415,  0.24222841],\n",
       "       [ 1.80340195, -0.21563762],\n",
       "       [ 2.1655918 ,  0.21627559],\n",
       "       [ 1.34616358, -0.77681835],\n",
       "       [ 1.58592822, -0.53964071],\n",
       "       [ 1.90445637,  0.11925069],\n",
       "       [ 1.94968906,  0.04194326],\n",
       "       [ 3.48705536,  1.17573933],\n",
       "       [ 3.79564542,  0.25732297],\n",
       "       [ 1.30079171, -0.76114964],\n",
       "       [ 2.42781791,  0.37819601],\n",
       "       [ 1.19900111, -0.60609153],\n",
       "       [ 3.49992004,  0.4606741 ],\n",
       "       [ 1.38876613, -0.20439933],\n",
       "       [ 2.2754305 ,  0.33499061],\n",
       "       [ 2.61409047,  0.56090136],\n",
       "       [ 1.25850816, -0.17970479],\n",
       "       [ 1.29113206, -0.11666865],\n",
       "       [ 2.12360872, -0.20972948],\n",
       "       [ 2.38800302,  0.4646398 ],\n",
       "       [ 2.84167278,  0.37526917],\n",
       "       [ 3.23067366,  1.37416509],\n",
       "       [ 2.15943764, -0.21727758],\n",
       "       [ 1.44416124, -0.14341341],\n",
       "       [ 1.78129481, -0.49990168],\n",
       "       [ 3.07649993,  0.68808568],\n",
       "       [ 2.14424331,  0.1400642 ],\n",
       "       [ 1.90509815,  0.04930053],\n",
       "       [ 1.16932634, -0.16499026],\n",
       "       [ 2.10761114,  0.37228787],\n",
       "       [ 2.31415471,  0.18365128],\n",
       "       [ 1.9222678 ,  0.40920347],\n",
       "       [ 1.41523588, -0.57491635],\n",
       "       [ 2.56301338,  0.2778626 ],\n",
       "       [ 2.41874618,  0.3047982 ],\n",
       "       [ 1.94410979,  0.1875323 ],\n",
       "       [ 1.52716661, -0.37531698],\n",
       "       [ 1.76434572,  0.07885885],\n",
       "       [ 1.90094161,  0.11662796],\n",
       "       [ 1.39018886, -0.28266094]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_f = PCA(n_components = 0.97, svd_solver=\"full\")\n",
    "pca_f = pca_f.fit(x)\n",
    "x_f = pca_f.transform(x)\n",
    "x_f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.92461872, 0.05306648])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_f.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_lfw_people\n",
    "from sklearn.decomposition import PCA\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "faces = fetch_lfw_people(min_faces_per_person=60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1348, 62, 47)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "faces.images.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1348, 2914)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "faces.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2914"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "62 * 47"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = faces.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(4,5,\n",
    "                        figsize=(8,4),\n",
    "                        subplot_kw={\"xticks\":[], \"yticks\":[]})\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    ax.imshow(faces.images[i, :, :], cmap=\"gray\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 2914)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(150).fit(x)\n",
    "v = pca.components_\n",
    "v.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YN9ZDC1A4wfiY1v137QdUatpYJlAvhmsl9tTLthjDuZ5XdkxttSHB0bbx/NAcqI0znSMdxIOxXC47xSTt4iBa9Tpfxe+tjnB/z7PakXOBzC6SATyNpE8QaAUR+uWkYIp5UztbRvIPcdRt6G9ToEzKt2WEHtOq16TkoJdBraUvX6/ldLsIq3qd8DMY0+/W4xHZ10T/ieJbgSuBhgGJ/8/1SfS7SAtVZ/XCtfPTqiy3BaQMSq3kmcDJAcv6+Qjgy+CHbKpUWoscbU/WnxOKmTDPj/EYzfHxcadTYpJ92gu4+lbbKelvSCvRWR8+xjHMVVwygr6OY2jrHkgffwTQPj09rdmfx4/k6cciq2otkbnybRUXXMPiBYPeXYjxclV9fHz8Zp3EH5ZAXc0Nh8MuQA0Gg7Vn+DxgnOPHXhIBUdXY6FCaS37mFTL4+rysUnfZjqklreMzub53zU1o3A6HAeGwmyi8RJb/UOf0Nf3836bkye9OJK2K2U7H/5+enjqQ4ERhmvq94N4XMKDPqnqzFH1bAMd+bVMOppsAQ7IUtDer6db9TE/vYlfZTycvJ00HmAw2rQqgxeRwzW2BNOW9wNtX0CXrJrg2wdabungrNu81zHnuG/3L/WAd43g+mP1TJ5PJm/8jXNdBeRfJsdhUPdvfEtAkyMlP62kJJ1L6s6kqQ1fpF336mI8DJgDMKjPBK2PlNtmeub7HxH7LhiiAZWyIvvE9zNUuxVevBGoHN/2IMlA+huiN123Uns/guq40yPq5n6QVmUEqB9uD1ZcWc7uQrIyTRrLB+/esrF2FGOUAFrzIxf1BWlTGR6psJ06u40TpALqNrs3vnPyykmxVSImw08lT/7v2kWujV5JoKwg4IKVdZvLxht6ZQFuPb7ntSbFlheit8naVBGep01ZSpg32MT72m6paAw2+VlZ0raDYmuL4hyRVLzxxjGFvbr/ggpiTtpQggiDqHWhIovjl8fFxt9n46elp11/vPmS/Jsb17WvLhvwoSlW92U4yx9TXyYrOutgElDNecg6/Gwj3Ecc0t9n/y3gIEDEAMCjKmMCY8NNVp6n2bLvZCnSc63s2Se8EenR01D0bY5TlAXl5eenmSf3GDW82nwjNVYvfPJDBBkVjEPlsGMa9XL7u+jKZTD5UgWZSceB0pegAuunxnqyMs+/+3c6zKbnwv9xebVfBCUyT5MrUnAt4L0lbP4yDq230SLLgul7olX1sJfJdpFWxLJfLjkKiPaboYCtyUwWQa260wLU3VRAGKnzfApCcZ/DYp5+20fw+bbSVvFvBy3bXsk9vSZjtNXgwaMjKfhexH9Cul5eXLsDd39/XfD6vu7u7urm5qZubm5rNZmsJNMGm+7dcLteqVs7jHDawJ3ZVfd9l6OTkZC1JmtLNym6XPnIOTB2rs111AQK90UuLTSD2AAa8Jzn6aI25FyohBwcHb96I4mTdV/Jc06ouwBxH8y1OvJnHb4+h3d61io/3Tkantke/NWs0GnVv1lksFu9OqfRKoCS34+PjtURlbt3o8OHhoUODJFM7MUnUCMO0CcpAid45puq1cs0gwf8xxL5I0Cg+0aXvl9UT/W5V2r5mK4ma/jH6QsdG9QYhuyS2lhhsOIkwvl5Z6HtsqmqyH/47aUqj/6rX8edxBduUF3j0ddpMRgRiI20nRG+ckFv9OYnmHp4OnujW0xebgsGmKY2PSCuJbZsOoJ0eV/ptP+Mnx7YCdjILLRtpUXS7StJpTjYk0Nls1n1ub29rPp93Okeyb9igAb6TDf0ejUYbx8uLHwnirmZ2FYI39jEcDrupD0Cm42Hu1530LrbmN2Z5FattGV20dJOLPxkPwEOfuGO/Xq1WnU+dnJx0iS6TKHutwy7QNl7C4DU1g8H3ab7pdFqTyaR7HRw7WdEnP0HiGMq1np6eOptaLBZb80fvCjQrk9xUwe9zTOexGJU70FS9bsTsQcSYWku6PZ/oh+b52ZduSPrL1RHtsnM5WHAcg+QEnMbuc9ETO/BsSlBV69UENIOrqvfEycso1AHUG1rboXyNbGMuoGh93Afrm03/7WRGzX2dlTaS3ECpBoHHx8d1cnLy5pVlTrCZWAg6nk8hCDG+tBefMC1oFL1YLDqAie33rbLTTrHRrIBaSa9FZbvS9ubonOexTUowE7Ft3P7fpwpl3Fx9JsDKeT0+pi6JEdgD9p3rNNAnY3tyctK9j9NBHt/z3sOcR5DeVczmjUajtd1v3BYzI+zOxKIXjyvXAxjMZrPunbvo4OTkpEs4qRN83THPUwzotK8QE90v9DudTt/sdWyQZGDkT256QAK9vLysT58+1enpaY3H464oge5nzNGbGSuq99vb27q5udkK+D68E5EDGt+xwbwHy06FQW+isehM656cR5neao/L+UxMfSWpsaTHMnD5477YMdyOTfOKTo4ZaKxHG7e/20VcSXuOK5OqaQ+f6595zaR5XC2kUzrBmUXA0AETSJ9xpG8OmqPR9zd6gEwnk0lNJpMuIWaFlVWvmRESqGkiQIzn5qgm6IsDsQMSwPMjgakF4AxYNlF9rqAcKAnM/O25R4NdP2rgsbT+AVVuZ18hgbh/m6YeYBVgnmB0Dg4OuneJTiaTOjk56dpHgD4+Pq75fF4PDw9dHCHAE9yzwnMARw+8XrGPAIRdoXlMDHAZn5OTk45l88YN/CSJOtkMBt93doJRSAo3k6djhfWb1f17slx+fxEJ1TP3hA43rW7w7nPv7u7q9va2rq+v6+rqql5eXroqETsZDAY1mUzq8vKyfvjhhzo7O+uYLca1qrpEapof+6QA4n5/eALNuRRuyLtBF4vFWuVgA0dIoDkHgyKMhJMWccBhcM1pMzimW/o4roORg5D/52Or3lZUpg9pm6viDHjWkQfSg+eE7YrjIwDBukPScRifViXj8fffvlYCAVNxBFsHY67j8feCjD7zSrSN43HW6XRaZ2dndXZ21iVRB8gcN4M9EDsJlPdTUsUyZlBntNn9rVpnOLwogrmdj0omw5a9eKw81rSDNrUSAceZgs7E62Oxa3/X8pf3JM9zxWD2ifEyeCeGTCaTOj8/76oStgd8eXmpxWJRt7e3dXt7u1atAQJajz1sqszNXvTp38vLS5f0M3m5WqJPBH7rgmoSinM4HHaFzWw26+jKXFuSIMQ2MhgM1qY++F9fIEQSrHp9XaS38/MUIEWSgenz83Odnp7WZDLpwN3d3V09PDzUzc1NZ7OfP3+uw8PDOj09rYuLizo7O+vmjrnOYrF4U03nUySwCPf391tttXcCbaFRzw/kMmOX5G4ICY5rcR4GS3CCEuHephlwZs+VOcmCHvsgpap646x8Z2fl/0lh5/GmeIykvRiK+xhdek4wk4wH2khtV/E17Qx2kJw/c2L3Nfi9dQ8nzdw4GrtJXRNImGf3gqxN92oJCQMbs01ByaFvKlFXGejh8fGxewORQRDVLHMtJA/aDN1GwPK8ONeninCF3of6Q5w0syJ0Et00PoBTv58UmzXAzXmpTKCwBga/6MXTIH0AX4vpyOTplyB7nBjr09PT+vTpU33+/LkuLy+7qmQwGHTzXTc3N3V3d1eLxeLNoptcPATg4pMMiqnrPv20fgyuPcaeBso5TSo54tBsNquq6qYMzAZwTY+/K79kkACG6DuLhF36B0AEvDiZr1arNVsxUOUe6J+k+vT0VDc3N/XLL79062s+f/5cj4+PbwAjuhuPx2vvsYYiNkPG/bjHH55AQdoo3qgPo/Lcj2k/Uz+ZCF9eXjp61p3HoDMBOVm72jFKJMj1CbxGnPk/OwpOa9raVVIe32pDVuZGk4+Pj29WRnKtlL5VaNJOpnEceJPK9rjYyRKR87cdjfMdmHIOiXk3VxT+9BFXejilF0ocHR11tN54PO7mlThnuVx2tA/JDbuiWjg8POyCKn2n3ZPJZO29uSRj5qaqqqPhjo+PO3vqK9wTPaJ7V78OxPabTQuYcu6XcWtVYabpDVawK4O0TX6wSTxFUvUKyFlww5z2eDyuqu9BFtp2PB7X2dlZnZ+f18XFRV1eXtb5+XlNJpOuKlksFmsLRjyvSly6v7+v5XL5Zu5xMpl0dmP/pE19E6h/px0G5gYOnrfEBpmOIMYmNcrcp209AbF9leKFROIqdFss2tQ/quKMHSRLAI8rT3yO+IovwRp8+/atfv311w78ff78uX7//fe6ubmpk5OTNSao6rutssCMdnFds5VmwP6wBGrakPkd0DkU2Wq16jqLgnix9d3dXbcaFyOjlOYnDgdvT+n/8PDQVQss2vB8kSlhgsHBwUEXrPomUCM9FI/Cc2Wl/6ZNOb9AJcS1HOzsrFTyBgOee/C1HPQyiW2TpJy4tuf28jj00ZrHMnhJ+pDftyVeJ1vGzRXow8PDh+bODIZA11BDk8mkzs7OukUG7ruDAxUj87Iex+Pj47XVjaZoTeXhGyTK+Xy+Nl+aq3/7SIvyyyrU7UnQ4goSnTlxmtbGntlAxYmbwOPqy4E7baKPMCamRgGrvMLw8+fPb6YHCMjT6bTOz8/r7OysxuNxFzs87XR+fr5WgSPYH2CJaQeOJdhn5da3OrPvok/aB/VqMJPz737EquqVrWMDCOyTZ1kBjZyL7TvR5dhVvX0zy65iW2fe2WwF48u4DAaDDnwCbrBd2IK7u7uaz+ddfri7u6tv377V3/3d39XZ2Vk9PDx0cYR89Pz83D2iYubUcdcs2XtrEnpXoFXV3RjjA53QuJubmy7LexLbaMqr2zAQJwQStBWYKx5xKNAK//egYey7VmimV504srr14iAMAdrTyNy0BEGFwEwbveAEasFBjnbRRwyd/vUNSjh5Jk8HKjuOHddUNrqgr7AI9Nfj5OtSabpfRv20LZ24r5hu9SM6zIN65Z+fReM8xgI7v7u76/TN2ILin56eOts0LYb9uV+ec0qQ0WfujLFs0ZyuOD0eCVYArNjlYDDoqpNkJLyIhWv73h4vMxpeJdpXbAembQGQAKSkzJNp8Dw3wZzzWcnKdW3vjCWxAOaLoM052MRHEmiOI76Eb7nqNTWe6yawTU+fUYXTJxbQEX+pUhkjkjdAMeeYbdd9qXjeJU0xxNiQLDNGuFDzKyoXi0XNZrOuuGCunsLry5cvdXJyUrPZrE5OTrp7u+iDAfIcdwJhYvkfVoEacZJEnMHv7u7q+vq6W24MQqQ8ZrC9igyqx9dyye1NG0xxOeDgIFAzCAp4j8duyTa03KoucJpMKq0BsDGa8ktq0wbqaxD0TLn0STJZeaQj8j19M8L2+Rh51eucZmsBBzprVWbog2vYvtJB+1TZJH7Egd1Il8DCmBCYWWzASjzQrhdn2L7u7++7YJRTHK76AJWmdU1h963SXA1s0k2CsEzSDpCmuj1eTopUoCQY69YJ17blwN6nejGAczKuqjUKk3twXbfFlRnjkQuhrHsnYCdG64Lr2k7t733HMdkbJ/FMmi0bMz1KOzgXepuEStXqZ75tJ0knJ9vgPu/aR5hE1gcwPqPRqKPOkxlpTStUvbKNo9Go2yHKifTu7q5+//33Wi6X3Xd+JpZxNw2eII9V2u8xQh9ehUsyI7nN5/NuJRs0rSfjbcimzwg6DsA2ChTmlVJVb1cYphg99Am87qfnCX1dBh5dsKCEBMriGD4OcK1k4YRqKtR/c76DE2j6IxVo3ssfAxPPC6YNuA+tRRxuu8fMSTrnRFJXvkYfxMv1PW7QU34OLKlPdAoldHV1VVdXV51dkzj92AnMAZQY1zBSx67NrLBgxf3qW4EynlkJurKtet1QO9kFzkfPtm9f24klbdbJk6TVmkvnOn180T7utph6rHq7BSQf+s3/DMa9uYt1R9zBjjOGuPpCpz5mU0x6TwxSaHcmTyfwZDoM3AErptwBxC2ARH9T34gZJ09V7Squ+h8eHjoQ4KrZC0IdMwwcTFHDJp2fn3cJFHuA+XSOglFKG0FvGdv/8ATq4EaDrFAMm84b2Ru9TqfTbkkyCdTluukVJ05Xn/w0ivDzdWkEffn6pCpsXNzTTlr1+hqvROIONlX1xhAzgSU90qoY/b8Mlrv0z/OtmUhauiC48re31sp9jk0hZdKDCnPQ9n0TFKUT9xlHEgU69VyqxwvkU60AACAASURBVLTqtYLGee7v77vkeX193SW75+fnLiDbF1yFQuvafszYUH2SkPGdXHCzq2T1ZH3x/1Z1aJ1a76beE/x4TF9eXtYWmmTFmqyGK70+fUPHTs78bp+x7dEG+w7jwCpMgE9Wl4wDgXsToHNf/J0X4uwqrpZZIZzJNMfH1Kvb2IpZvk6rcq96+05S6w69+WmLvqwXicpbd7J+xm13/PM9+J3+ML99dnbW6QT/c8LO4gCb9vd5D/T8Xh8/9EJtEDXGR8OgY6FUfZ4H0isfKedd+UCNJC/tpdgkKjrqebzWnNZH6JRMoCg2g4OrQdpX9UoXeT4kDcUJbNOkte+ZQdKJrY9wX8/PbUKcRtUOQvn4gPvE+bTf1zV1m8nTgeyPEjuvxcEPigfdLBaLurm5qevr65rNZl3yxO5MR3I+CdSbKmSA936roGPTjh9hFOjLJp21klorgSKtOVquY7CYQC8r3/S9j/SLNnp9ATZvGj0raN/X9kjcyg1fXDW7YqVSQlpB14WFr9FHYHyInTlWBjBOgl6jYfrT0wIZX31u2oL7ad3nIkfWrXxkLFkkRCwxXY3f5CeBOPqCwiXG8jiap9Nc1ea13GcDFoOWbfLhBGoFO5lRcmPwreDJhL5Lc3fq4OB1BxpQBEmqNTfWMlijyX8ILeYgkWgm0SiG7gl4G38iWVclWYlmQvQ8k0HLR8ROlpUw//ectXVqhJvnZzVbVWtJNelb69mIvhVo+1afBhpuqxONwQCLGXBwFq/NZrM3+6qCcN0HP9KUK5nRN/rJbR4NrvoCIR9vmtQ6tO1kQOaeRuYGhplAq15pZvc/j7P/YTcf6SNJA8Di67TsxIt/GFsnAe/P7ceSqP6IR8zV5crsFrhOOte62rWPZtKcQJN5SqqcNpmpM13tBOp5ZFew2Wb7rp+ZzDjRR9ImAZ1U+oAP7st96CNxj9/RFUkUffnZXDNt3oWoBexMl3tl8x8+B+pqo+otTWSntKOY1vOSay8yoXNZjYJ63PFEEq7evIrqI5SRf3If03WJami3++AA1boO3+f17JBZ+TqoESTQV9/ARFBpJT7+57kA92ETiNh0H4Qk0tKT9d7S1Xv3SWklUFchqQdW5THGfgEC6NvswnA4XBu7rGY9jcD3Bluu5AaDwVqC2NVeWwDP/U+WpDUvyXWs721JICvMlr+0/O4jY8h1PY5OxtkWr0vwokRXULk+A0BOAnVc4hEQWDLrnHF3gjO70rfaNsihDY6lrqzNBpmRQ7euRH19j0vGEmwwK05vsA/Y+Kh4Djd9M7dENACoep3D95tVvK0mOncSpN/L5bLbk4B2uOL1Ykk/2+sKf5N8aBFRVkuJlBCCUSYaowcbQqJplJ3/T/TpoGM0xmD0RUyptKTiTAdw/KZg4nMtTiI22k1I3TSx9e0+7mrcDrytOdjWdaz7Vtta1KCd0wHd/ff/8vrZjj7jiDNxTZzf1TUVpWn2pCYzEAIoUld5HHN2TiTYlalaxt+PLfSRll26mswxSH1bXy1951iYvchkuen69oNN+tokJA4H91ZycFBmvpug6RX8VFL87TloL9bx5gSTyaSb13b/sSnOZVyTuekj6C83OWgBHvffNC06yLb6e+7lgmS1Wt/VKd9Ok+f06SN6IQkyxec41qKgiXs8bsSTFsPhsBaLxRotjd4APrCdLbD7/PzczQF7hyk2muANLrR9k/SmcDNQ5v8ZbAcFvvdEOY1PY9hkNBg9AcPG7KrABvMRuiGroUzUDia+r/XhiqSVCOzwpox8nwy8BH3Pv3F9O8iu4oDmfqHfbQshWjrCgWk/fcgKKOc7jDjdrlYy7zuWXn0IDZhjZRtqzfstl8s3W4NlG6vW57CS9jZ4SADhfmV1vIsAQA1UDTzdBsTtsA1kcgKweQz4vxOPbaA1ZdKqjvpIsk6ZBOwPJE8v+iIBOGk6QXB+rqFgo4zHx8e1R5Rsr7TPesrqfNc+WveuvC30w4Cman21rcfU0wb4Aht6pG8RL704cNMaiY/0kQQHMAGs+nEig0H0QvI8PT2t6XRaVa8xNuMLhRnJkDhE3xaLxRu2xbuJ+TGflv2n9K5AGdhEQzkn4EFrUUgeEFcGphW9NR60WlZ/pjb46etltbprH02VJBWVukiqroXGjZANREzLuDJp3Yff3RY+fekV6zqBQVYtiMfSH5K62+gKu/XJBQxeJOIElZXuroLO/PyfxzRXJTLnQbvpj5NEJj/svGp9swZXKwk6WwmaINc3IPkayWAAaBLwtRK4fdhsTrJHGXBdgXmOyrZvG/0IW1L1uibCYLyV1FnIxTO7pnFpLwnUz+LSBy8goYrhHJ4YSIBkaVXifSSr2oxn7o9XwXpRnouIZJnoC5/WHJ8p8E3TVVVvX5ixi3COK0ToVah1g4PhcNjtF+D3eubTA65S/XgT1ScJFDtgZzqDFc7NF3C/Jx9OoB4ojNeLYrztmZ9pAtFnQMvB5TpWLhsy2IGoLPx8EMqvek1WffqH0TroZZWWwWLb9RxgcI5NwS2vRRDy9w7gHoNdBWf03J771KJkkyVwRZnJ3nSPK85WZZ9ghfa5rX0DLuJkCeORlb/nTLyoYrlcdq+AYjcTdOC+22Fx9uPj42ZF0eonuspHtHYRB+q0g7QtMwRZSdtvzfx4rs9gxADVbFArgeYYumrvM46ubFuJmeR5c3NTNzc33Q5pXj1Nder9q72IyGPq/bMzYQOQWh+Dw4+IQZnFTBM+y30Mhl18ZBWJL3ixm59WyDZkIm7Fhz7inaJY7GO2y/ceDAbdOJyfn9fp6Wk312kwxXhRSToJshoXIJxz4ta1AXcu0PrDKlAjai8YonF+torqk636oLcYfAe2wWCwttorDdzG4ErFTkogyICOcvqIE2hWIYnG89rvJVYbZxqqg62TZt7X1TX97huUXPlsomiySsmkl1XHcDjsjNR0PWiulSB9bgu5tyqYXSQDmlkKPulwLBZB356zJIniqMx5+Y0sVChefEBSSnsFlPHzI5UnbbNtOoGih2QZTLX7MSQn0Gzvy8vLmzllbId75OK9DEK2+z7jSGAj2GUypqJkU/jZbLYWi+xjHMe+3GaMsIfVarW2PZwrfFOH1j3221rduksf6ZcTIXGoqtZoZ7+vlHsSQ4fD11eYsYUq+8hSvT0+PnZvfMqpCEuCfMRA9COxlaLKi38MEGgLvuX9quk3ybWq1nZago5lk57RaNTZtxcFsmiwqv0stO1+m/SuQF35tVZSUTGyGw9BgoFl8+eq1+fNqmrtMQAMpbUJPMnMA0IF6621skrsU8HYEUgG7ofb0EoypicxFqMdU2Y4hleh5XU5J6nNFv26i6xWr/PTrRW4eU/a44DoigoEy3h67+HWUnl/MjFv0utHqlDT6+grn6PzlpIkP5IaAfXs7Ky7P0kTmsfL300L027eDpLUI/dwXz+SRLm/58scEDJp+fdkfTxuTjqPj49runF16mmS7A/AyYkBm+vbRz/CBnBzAiVmJAXoxT34WKti9ksGTk9Pu3fG8lyhV+ISC5BkNryoZRfBlwxoYCS4Tz4/nHTt/f19F3sYM/YQN01tZo2+bKPWk/3KPu8qHi9PM5gN8bx6Va2B2wS+JEm/AJ3xZi4TXQB67KuuYFvAnTa9Jx/aC9edd2A1NeiAgRPx7BuNxti9MT3GwccJKQ0/0TsBsrWAqE9walWgrXk79w/dUFkbwVpHXihiWsEJNOdVW9VnBsa+CTTnOfI6TtiJylr6NBL3vE1WX1mJ5hi1kmjfqoVzsTMSuKlIkmOuwOMcxtzzKFWvL+aGHsogYup2uVx24CmZA9oI0EQffSQrHsAdkkGWPnEv+4krrarXPaid9HwffDqBKtM2WWnb3nI+bZc+Al7siwlKGXNodPsecWaxWNR4PK7pdNolKc5hi1HmOw2q3B6D4wTL/P2RBEobSZT5vWMF+mit3jbwcTyhj8wnevMXM1KtuJl+a7/aVUwvEwO9MMsAp6o6HwMgeSvY09PTbltO77UOiMW3ZrNZtyEK8+Ichw6dW9KmW9Nqlt4VqOlMV3amvhwwyfpUoAQxGk45zQb0dkAcgoopy+lW5zI5vFeCt8TO33KYpDwSVVk/rtCM+qteVxabnibAWQcOwInk+lK36IiA6nmBrJKcQH2uf3d7NiV2QJOTi5Oj9d5Cg9muXQRKLlcyYo+uQL3fqNvIGOTqTB9rfWaf7QNOOOgKkJZj0ycoGRCQYGhHAhDflzZX1VrAB0y5QrHPI/YNjwvHt+Z6P1KBOgY4WfG3Kz4oQT9Y75XRxBooXo/BeDzuthclcHN/AJUXNdIuJ82cJuiTQAH+pmldmbrid7taQAidc10vippOp10fzSS4+jXAafm+x2JXoZ2eqqMvHj/HQOzZm80DHgC7XoyEXT8/f9+b/fr6ur59+7aWPKteH0XjHrb1jIXoepN8eA7UwYabZMBwkKqqNSVY+aaOnIjpkCvNTffMTlrZH0kyTn5GNwQCBytXmlWvRudVnbTHE/YEFi/k2VSNZNLMiqyPMbs93sA/ab5MngYjaVycl9fhfyTR1HEL9WUF+hEZDoddkHB7CXBOhE7uRvpVtRZIsU2Cc9ppC7CRmDiHYz/KjrT6SQDyPGGLSdgEJgn4CXxot6tcg19LAqtM1sl4fLTaNjA1pYfv+PV0xB6+gwXzGg10CJXvbRgNCAH+xCozY9ZJxoBdxNM8FAu83sttQWdUxNimkyuximv6EQ1X1Y5LnOuFoMR52xFtJS70TaCwLaPRaO0dz/TDa2IY8+Xy+2K+qqr5fN69puz09PSNfzPHzUsgvn79Wl+/fq3b29suj3gqAh3ajzN+tXKL5UMJ1AbsColBQ2yUOC+GYDQAXeRg5c5U1dq1E2W7k0bABATPi/SRDJYOJkkfWUdusz/+vwOVr58JyUac9Irb6Z/vCfrPuSO3q5XQ3Ff/z07lii8N0Qbp83ws12xRR30Eysp9MVvCODoR+k0pDpIE6KzSoUz9eEFWnhlsssLMfvYFQvQn53bcX/rv6sn3pK353JvtP5NFVlhZhaM/26511ZdNsP/Z991u2uSV0bldKEHaY2m/9jjx03ZDX5xAHSPSj3ftH4stvaCLTdfdDo+H7wHNbZvNaQq/99TAwCyU9eL+GAi14tV74pjvBArV7oqZa2IvbH7BeUz3mV2gL7CZv//+e11dXdXd3V0tFou1qpl7tFbcborNm6RXAk3H2zQH1KJPql73EDXiab3FIxXPdRl8G0A6Kgmz6u1zbLuIjcR9tQO7InU14YHgp2mrpDirXukLn4f4uE2Jxnrv00dTuLnbCMdkIOZ7/0QvphDpM4aNc/h67mveZ5tz7jqWVBX0NalZgiX3QRc4KOeQPJ2IEzx5HrnlG62ElfIPAQz0h4DgcUxgmUxJgh7anInT/XLi8Lhm+20rSeHuOo5O4pmo+HixknVhViEXSmUbWyA0Kz/rOtvUtyKzECupOq0nFxUJGgAT/J/qjXFj6sELqZwks3Jt9RW92uY/Avbs915sSoHFMfQPobiqWn+tJQvbGAtfl5XHLB7Ch2l7VW20YeeRTOgt6ZVAbSSbKqu8mQNPOitUaJ7nRLQJHWRFwHWtKAeMPkgp53kdzG2g7pMNz4jflGDOn3hFKPpoVbOZdDAyJ6k+YjotE6iNKFGnxQ5k585KwVWJ7+/rZDC1rjcl8vdkMPj+ZgacjUCAzqre7nCTO6+09Mq4Pjw8dOPu4OLqzLbTquJTl17Bu4skuDTN6mDndmeCc1tMUSctyf+y6uI6yZZkMGpRhB/pYybQlm+SNJlnwwZY4W9bbU2F5HU9R+fHsjzOHku3exeBLeGxvapqAvNsn3Vh5s/jZIrSc8+MSWvRUNoqesp+9qlAfV38hyrUidrXrnp9JaITOf3wfCkJ1AuUoK9hHJbL5ZvE6RiTPkMl/4cmUJ4lMpVDB6rWKUqO86DzLA/zoHaMnBtyIjLKN13mTy7CIcH1WRGHoWUg5H/WhWkTU9QMlpGdnSEnzZ0cEyQk/YagzwwAu/bx4eGhjo6O1va9BJ1npei2O3A5ebfoD1cdrUU26I42ZT/y2D59HQwGa+zH4+Pjm2eEW+AEe0nE6iRpWjaBnyugXLXaEiejvgsz8jqbFq/k/bcBkqzunCha1VYL4LTG8aOLiKpeq4GWLl1Nm/Gh4mRbPz8fmgupuL7HzvQnC4wcUL0yN+3zI7Y6Ho/XnlN00ZH3sWScymPMAPG37dhMmHXsYx1rst19xG0E4GAPbntOEzA1kVWy41P2hVw1Ho/XFoCRI7gf/WN9CuI4vU16J1CCfibQDPhGPVAI5qs9UBiu985F6KDLeL63kdrJHDxzl433JI3fgcSBlnYb0TBArWv5ejgouqEvnoekT06mrg4wOq7ZR5bL7xPzrQTaoryz/duCaDqnH9Pg+0xYXIO/M6km8txFHOQysLVAgo/3PBt/t9rlSgab44PNuwJIEJFgxMi7j9guWsl6WxXcCvSt411tpw5s5wm2ONZsTJ/kQgzhWUDvhkTf/fPp6anbQIBHGPxeV++Riz0xFjyexNoNHpf4/Plzt2CFwIw+DORb8/+7yHA4rMlk0k0f2P/dt2RF+N6Ucgt400dTsdafF/GYEq2qNwCfc/pUnz6HNr68vL7Wj0VNSRFTQVbVGivUmg7LJOqY3WIhHKutowSOfyiFS6cWi8Wa05qCpHPQSAyOE2YOnoNn3g+e+/j4uJtQJjBzP841sqiqLpC9V4anJBCwseQgeeGF2+9FUpsSsvWXc8A23KQ2WkmU/+8iLy8v3fNwTqAgwnRcfm9VpVVvX+Vmuse0fTq4jTzvlw7fooK3iW3LujS659pZBTLuWX07SbUW1cAq5F6a3DeZE9qZlV4fW92UiD02LcDDODlYu13ZP1cirnKtX4+52+cFa30rUNuBx8BULMc5Uc9ms/r27Vt9/fq1rq6u6ubmptsjl23+knb3gpvpdFqfPn2q4XBY5+fnXb8MUuwP71WK22Q0GtVkMulAbc5hm2nyPCDxtQXWDNicNDOeuFrzKlizZvaXPv2yECtHo9eVzMQe9IefrFavW/QxR0rffIyZvrRf247nXO/u7tbe8csxrMw1a7TLlMqHKlCjZQeAqnXaNQMwHUVpXlyzqcIwBYthQcfZmFwJYxj5brhdJCuFVmBywvR39L81wFnB+bk168LXbyHOVpBET336OJvNajKZdChwsVisoTMbou9l+svBm360qhH/nvSXkSPXcoDIhQN9EqgrUH76cQGSZy4KyeTL9TJZ5hyhk5SZEyePVgWRevyIGDFnJeS2u33o1fpwQjAlnUyLGRlTZ1Tvrljxeb9erG8FSgDOeJPH2mdtdyRIxtOLw/i/ARAfHoHheui61X+3Ib/fJsPhsE5PT7vVpQliE5in7fpxLFeU24CnY5Af9fG4GWRmhdcC2e/10YWME3smUOyLXMPzq15FnIWJ22LAik7ZvvHl5aWr8tGz7bwVC7bZau8K1NsqedeHlEyGDl4OjKlgGz3owcnJ21kZJdmpTKl5ldeuYqNrgQTTfnamrBB5Lo8EnqDD94ODp7JMAYFl1Yn0CcDL5bIzLGgj/vZcaNX6QhsbbitwGAXawA04YCs8t4DuCAy2D1N/fR5/GA7XnwMlqJMIHCD45LQE10H/WXG2aMoMfq4a0mYSfNHOPiDBVV/aH/S5GZ6czwSwGOwlhWWKsgWMDJbNOGQF4Pdx7iqr1ao7h4CalRbH0eajo6OaTqddZfHp06e1Hc48TrZhwLbnPtl4gB2pWvbNuPr7PiDBCXQ+n3dUo8fZVb8rN4Ditg1BHGer1ucI/WwoPpnsWVZ5jrO7SgJnxszshSvMwWDQba3I72dnZ3VyctLZ7KbtTxnfh4eH7m9+d4zxeV6t7Bj9nj/23omIpPT09PRmT1CjWwIHjsrA0gmCiqkYoxDvjWu+mjkO9j9sDdTBwcHaHIYD6XviZA06cYXBMVlJcB4Ixits6Tv7VbrfBhJJP1S9fW1QVp9GcLvKarWqxWJRd3d3a8iXT85Fp06cFBNlu212YGzh+fm5A1J2cl/PW5YlxdwnubBgjUDKT1P/aaf8bcfJxOTk0+qvxy6rzEwAPq9P0HU/abeTvIGDp1Joc06nVK1vlJGJPj/uT+t435tKIBeq7SKr1arzm+Vy2b3pxlSg72uANp1O68cff1yrQn3drF4yUfmarky4Z6sKor+p220yHA5rOp12CRSKOZkuv8prm76sE1eVqSe/oSgp6BbQoK/vLYxrCfc0O2Ffc4xdrV4XGRGnmEbIF2R7ZbcZTV9/Pp/X7e1tR+MzDVhV3fSgp11aPrpJelego9GoTk9Pa7n8/nJSo5c0Pg8KA8ZAkO0Hg0FncA5UVqLnK1Aaf2dVAHVL8pxMJmvt2kUwHmiSvE9WHYnIXGn6eqAiFjiwjyPBxdtbOTDZcTclsV3pItrt9yaSQFlkQXv8QlrOy362xEHdASZX4yYgScrWb1DIjcJ3Ec8vG3UnDcXvXN8I1UHHlad/91gbUTvpuqIzxeYxbC3gek88Bg5C3KNFwdkvs39VbzdHz98zCZutSLv31m1+jGRXIQ4YlJjKtU0SmA1c0/cNWpxEbePZH8ckbLdFjdJfaNg+CZRFRKenp92bYrgGuqbSxHdIRrmjlsWAJtkHznG/6UNrh7JcL5AAcpvYvsw4ARzRA20EiCwWi6qqbuMEM0hOoH4EzdfzYiVT5KvVqkueVOFuHz+zek/pXYGORt9f7fT8/Fzj8bi7uSkET86D1Cihq15XVDlQmjZEIQR3GyNBxpSVHQaFnJ2d1XQ67arePgm06jXwJCppceN2OJ/rwJgPc/tvL66grw5E+ZwoAd5053uT3ZbV6nW7MCdNJ9HpdLq29WAGTdrD9dAxbXY/TH0ZdFiP6RCuPHm7T58Ek0iSQGPJ6j3nBZ1gTT+nLbkfHodMThnQbSMOWLtKVoCtKtk0uI+tertyPum5TZ8WmEwazf2C2SCB+vj3hOkG4ogXeGQVlBWwxwYdZLVicZXuR5H8+JPBNbpj7D0/Cfux6zh6o/fpdFrz+XxtbOgHK1aZlmrNxyewaIGsBHMUMcvl+nx1Vtn4S47/Ln1kSgs/IQ49PDzUdDrtxtVTfRQV9/f3a+01tZzTPHyXwNzxxT7Js6KO385LfxiFy02hUsbjcY3H4w49MVnLm0ic0XmYfTAYdJ2hoV4B6krN7//EKDK54NCmbc/Pz7u3Knhl2a5iusO/2+iSR/d5VZs3os8Psik5pMF4jsUJl/vv2j82AoDa+PTpU81ms7Wq9OHhoQtUiR6THmrpLNuU1ayd0gab1C0J1NfdRWwbtkczHIk2nQgSpOX+uTl1YZCQ1Y3HP8cTMPMRkOBxMZj0ikcDFs5r6TEpZfsYf2fl4Wu2KGloOJLnRyjc2WxWVdUlMmzPTAfSmn/lp5me3H/atpJzoe5ni9q0TXuBVZ8KlNhFTD0+Pl6b5sEPCfS5uC0BFNICewZZrqq5F/rxfL7Bpv1hV6HtFFIGd9yLRUKwRlWvQJw5cCfuVhU8GLwymlTM9M/xcjB4nTt2oeeCZz6fd/Ftk3zoMRYGFPqWKpTBd8cZIC9qsAFmAmhVYYnwEBSB0nlHHG8wpyyHN+/TT1dG6WCmERJ5V706G4jLrzYjMXhOZZu4avNCj0TRfSoXkgcV6N3d3drybuZhJpPJ2qrrdMasSBF0lguFsp1Zoefcp+fN+s4Pcv/lctkFXjMFZjtoC987KfjBev/EDnJBSyLjBBeu2JLiJMH06WO+GDkpPSdRrp2MgoOwkz/jiL8TZAh+CTDRI/Zq2swPzXsj9/dkuVzW7e1tV7VQSU+n0zf3RSeuJJ0YzGy0FiFyHkVCqy30zdMRDtLotM+0ChXo09NTx+rBVngXMzMqxNGqV58y22Nw0QL1Odb0JXfjSnswcPFGJe/JcDjsHptjvPARwCNvWMlNKmxztlevqTEIdx8M2MwMem2KqV63DVv7wytQHImValC4VKKr1aqjXpN2rKq14J8JIQ3RybVF16BIErnfd8fcbN8EyvU39Z/EaAPj/65GTJckbZLzRRYPmPXn5OIJc4JcnwRD4oBeY5n37e1t3d3drb1MOOfV7IQtfdlOkinAdpxsMrh5zgwKBzvZVaC5nDQ9ZvkoTV7b1RxL/TMxJYXJvVxhkZgRBywnT79Avk/lQlAykGLqgUUn1h9j4/Hz35uovwQIBiFpy65kAGNehetFHO/Jcvl9rQXBk0WFz8/Pb14WkKAAvecUAjrIFdO5AbvH22PM2FmngNLWtd+TwWDQ7ZiTL3Z38nfcQFpAzVVismCtcbWuTXX7Hsn8EXd3ZYSwVRYCAqL4nWkjQC9xoRVjzeTkVJd9k8TsHOPK3fHI40Xln4/BtaR3AqWRBKfpdNoF4IeHhzo7O+sCBJIruRLBmedHAQ6yRiF02IOYCZSkTjvH43HvCjTnWRhAqIhNAbNqPdjkfKWPtcO3kqn7DnI3veJB37YyryU4pudCZ7NZR+mSQF2B0n/Opw++Zuqwav2RlarXZeZJRXvltYMux/Z9jMW7mBisGc17POysTvwZmFv9zfFu0ZQeSycYgIIR8C5C4HW70K0rZ8BVAoWcP23Rfe5/AiK3w0ACNE9cIJDxXZ/V1KvVqjsHWSwWtVwu6/Lycq0KMTVpat0J9eDg4M0CGY4x/e2PgTzjZxterVZr7/AcjUa9quzhcNhtFEPccvtJaqPR6A2N6erR98O2HcdyvFyFVq3HaXSa44T9EFv7VKCTyaQbe/vkYDDomKaMuY5rmRfcP1OwGS/N7qBH9OB+oUuKP94r+4clUFCEUTWBACepeg0AOI8Hwskv6RcrJhOuEyioD3RI9QuFDJKp+j7QKGIXyYBpxMdg42gOuAYCrYrRHxup0aL5dlcNUCv+5KITJ/ldhXYyT3V7nh/4GwAAIABJREFUe1vT6bSrQieTydpSdwBUC9H7mq2PdZsAw8mTYGmjJ2D1rUDH43EXzOw8rtY3VVqee0+HdgDLCjSDWaJ/J5hMnn3nBwEJriAJtjlH63vnNdCDg3aLPfDH1VDSvwZCxAVixGw265VcqFBms1ln7zc3N935Z2dn3Xi02mZ7IAE5eCfjlf6YMSqnUgB4vDYLHxmPx70SqHcTcrtJBiSK9EeOoY/uazJg1olt3nbbom7xVd/r8PCwW/izi4xGozo7O+t8j+ddsQWYMPYC4F5eXDocvj6+8vj42BVQnvfG/nkkCAaEOXiPieNR1fdcdn9/X7///nu9vLzU5eVl9yTCJumVQEejUX369KnrTNX3cncymdTZ2dna2w8yoGRQIBnl4PDxg88OwgRvDOro6Kgmk0l9+vSpq5pA5ZThfQa6aj14mPPP9puadrVctU5Tm5f3QhGOtZE7yLlyJQh5k2xTEn2oP/dnuVyuUYjeeHs+n3fP3bVWPXLfbVR0Bhw7qj+uxrw7EnbQJ3lWvSLe4+Pjenh4qNls1lFjuRemg24mAuy5Rd06iRpEIRwPQ2LQ4A0s3Oe+1B/UMkEkqT76BpLPa2cVjj5cteXPvL7BtOevSZ58b6Zq1z5yXWyTKt2LS/B5+gMQ9T1cjRoAJ9hJ8IzOzJqZSeBxsJubm5rNZt14O/DvMo6ep7edYIskDa++dbWd1bTHLKvytFmujf3RV6ovx3R0cnh4WGdnZ2/YpU0yHA47dvL5+bm+ffvW+fhyuexelI09V72yZBRm2GrLxhknjk//crHhZ/SdfB8fH+v333+v3377resrbd4kvSvQi4uLtSpqsVjU8fFxt/TaCTOD5nL5uqAjS+M0nky+/hiNjcfj+vTpU52fn9fFxUVdXFx0859QI0Y1u4rRHOe7OqVtrBjzd6ZVnARNI7aM3QHPVXmrkvUc6HK57LUirqrW7oEDuVIAvbHFl5+9q3rd2ce2kYjOemyNs4EBCDTnP41Ss1p8b/zG43ENBq9L/u1YTqAEmXxGtMWEuLLL6tu6oKrwxvIERAJHrk5lrm9XIYFWva5QpfpE166ucsqkqjrb9fi5Dy37TFuteqWO87lPAyTm2PskF+Tp6al7xOrl5aX7+fT0VJeXl/Xp06eaTCbd8Q6MiCsbj3+yKcmwGAj7ucPZbFbX19d1dXVVV1dXdX9/v7Z1aJ8+GoSYhnTiHg6H9fT01K1LsM06dhrQtsbWOsipIScaxy3GEsZjMpnU5eXlzgl0NBrVDz/8UKPRqHums+qVpeRxElijZAAytmYlbR+1HRrEVdXaolfv+/v8/Fw3Nzf19evX+vr1a61Wqzo6OqrPnz9v7Vfv50BBe/P5vKvuHh8f6/DwsE5PT9eSHIaYnXeQpfFOCLmgqEX/ovCLi4u6vLysz58/1/n5ebdnIguHDg4OOhp5V3HQ4G//r+p1he2mubFtFaGTse9X1aYUCUB8TGv68Y4+lBEBnfOg3FwNzufzDozkAigHadptdsDJhWCWyQnn9VyZH13x402r1apL4rsIyQXabjAYdPcCbOBU6IMqkUeu7KStxJGIPul/phdcETmJe0zps3W6izA2BCSCncENfUD3yZYgm4APYDcpUV8zF4FR5TvZsBNMH5q66rXyYJqB8fHCpMfHxy6JPj8/d8yJKfkWqM/Emb7oc0xLz+fzurq6qm/fvtWXL1/q6uqqXl6+b9vJBi59pdXWXIFO0VBVaxVUAiNLxhPHYgMD+xrHEg9ms1lXKU4mk/r8+XN9/vy5VwXK8Xd3d10iZlP3weD1WViKHjaNcFHlOUwzRklD0w/GFAbNG+x4MehisejG8tu3b1VVa4tiN0nvBEpHoUCoUA4PD+v8/LzrHMHFnc+FHC2K08bNIPKTahDa9uLion744Ye6uLjonv0ksLFyEt78ownU8zv0ieqrhchblZIDq/+2w/r/pp+Yo8zKE515rq5P/3jODDGtSFCiQvL2aSRSAyT32VVoon9/T2AlUYMUcyWuFxoYke4iJDDa4XdDktRwXlZs56uVnDBN/XiBSSvwmjKrqrUglc8jAlgcHHYR/MEMyfPzc5dospJCch7IY+SP7RwaOBdgOLDZh+3zi8Wibm5u6vb2tpsn/Mh0g3fx8rwowGg2m9XFxUWdnp6usVCtZOEYw30SEPF9JhIq6a9fv9Zvv/1WX758qdvb26qq+vTp09quNruIx8fx0vfl+6Ojo07P2CpgOJmrBNQtli8ra0AlOgMszGazzj8uLy/rp59+6irKXQT28vj4uG5ubur09LRb4HZ1dVWr1aomk0m37zDHeprEu1i15qc9ZtZFTudRZNHHh4eH+vbtW/3666/122+/1fX1dVcxv/dYWa8EarSWScBL/Y3u6BTI2CU1CcDop0UzmbIFQTh5onRTG7xhgPP7BN5NzmT6mGooJ+ihyvJ6tKOVNDOItRCodWPKlcqgj8PC7TMeVa8UiRE9zuNNvJ04NtGXGYCq3lIsJBI+gBzsgf5hQ9y7bwLlUYeq6mjS29vbtSrUrEkCQPfZz4B64+mch7EuTMElVW6gwvqBbczFpj5CRQEW6SN7iDpwmhJLsc+RPE1X89PJFR225m8JTre3t3V7e9slvl2rlqr1x9WgMLFL9jVlfvT29rbm83ldXl52wZjKHGbBW4NaJy02wfQ0yfv6+rpub2+7auXXX3/t6FvoQWLErrZKoqx6ZbjsJ14HACj0oy6pL4+jx8u/U1HnAjbOIXlCUz8+PnaFys8///yhBMrjhVdXV2sb3Tw9PdXXr1+7zXmgcmEZ8UN8ZNO0kOOL53C5P09kQBNz3PX1df3666/166+/1tevXzvmbZfplN4VqBXtQaHq4yXNzA8SaEA6pmd9jTRa/gfKZqXtdDrtaFujPZydCtVVY9/A25r7oT3839StKVEPmo246u2ONKYg8lgHJVcFJBijRbdx1/6ZLTAazQUbXvzEzkSmjrywhms5uebCIT/I7gqTvuPYrgBJblTCu4jBV1V1zsMWj1Cf6BrHxJ68AAjk7ecCvS2f+5tzpu635wOpQqny+V+f5ML98JHh8PXVT95Tldc3bUqiLd/ISpSPGRjsD5t0PGAcve8zx/QFswRVxmy5XHZMid8kdHl52enz06dPNZ1Ou/GkOvcmCgCWLAZsN6vV66Yjt7e3dXV1VV+/fq0vX77U169f69u3b3V3d1dVVRcXFx+KN1WvNuhxdf+IZVVvX3xtWzSluW0+37ow+Mlq+/r6utuR5/T0tH766af6+eef68cff6zLy8udEyjjSOxhug2Ae39/X1++fOkKH4ox6FZ2MXI7Wz7nosMxBJ3BnjKuNzc39csvv9T/+T//p3755Ze6ubmpqlrbWnDbWPauQO0o/A4CBu1dXFzUwcFBhzxN2YxGoxqPx51TMXjm+u3sBE5KbypQKICq19cQgVag4FyR9pVEpXyXxyCtiXp05gSxbZ6iZRCIE5zpJ1OquwrOwP3y2aykULkngZJ9Kd0nj5cdl/MIBp7HdQCz4wJEoKuwMYDRLrJarboN8f1Sdu9UxaMHnl5gnsePCxiYuQpNNiFRf9Lt9N0vESB5Wn99+sjKTMAFQPPs7Kyr+BKseJw2TQFk4uRYEhjJtKrWrsvfBGCqQui3weB1T9RdxKAA/7+6uqrlcrn2iILfJISteUMVgyUHWIPi1L0rmtls1i0wIXne3NzU9fV1vby8dDuf8fKKPuO4XC6bDJwByGq16qbNzAq8vLysrVHw1EpWnK3k6Y1KOI7Kk7GDXv38+XNXfX7+/LnOzs56A3fyBE9NAGZZyUwVbz+Dkj85Odm4INPUNDZKfAEIAzQAYNfX1/XnP/+5/vznP9dvv/1Wv//+ez09PXU2Q0X8hyXQqlcq1kkgkZEpN/5PkmUFl3fASRSUycE75nuHIYzJuyERfCnVPZ+1qySF7ArSSBWDyGTHOa05pfwf121RgQ7EfqTCTm9n2pX6Qz9uE1y/qyQvBjG9SCKFrnewbU3se24z6TP0QYVLQMeWOA4b6JtAoQyh9V2hTafTDsiR1Gkz+qEtrWTCfVyteK7NCdRUoxcR2Tazmn1PQNvoE19hf+rT09M1qjxBKrZAu2lDS5eugHyMGRTPKTFXOJvNulXP9I/HPHYRAi7jhp9Dj5uys20+PT3V+fl5R+NiAz4n40KCIfsCNJ/nPGezWcfKsC7DO1btKtzLzz17kSAgD1A3n8/XbI6qyp9ci8CYp21yb2za6wQWi0WtVt9Xo56dndUPP/zQTZsBGPr0kRXiR0dH3TScWcTFYlFXV1fdlBxjzfFeWe25W68cxk4T1DtO3t/f19XVVf3yyy/1yy+/1JcvXzqaGqCCH733KsxBn/mWwWDwW1X9zc4n/N8l/5/VavXTewft+/h/vez7+Pey7+P/9bLv49/L/7/2sVcC3cte9rKXvexlL9+l3w7re9nLXvayl73spar2CXQve9nLXvaylw/JPoHuZS972cte9vIB2SfQvexlL3vZy14+IPsEupe97GUve9nLB2SfQPeyl73sZS97+YDsE+he9rKXvexlLx+QfQLdy172spe97OUDsk+ge9nLXvayl718QPYJdC972cte9rKXD8g+ge5lL3vZy1728gHZJ9C97GUve9nLXj4gvV5nNhqNVryWLF84nW9z3+Udmu/93brGpuv6//l+w8FgUF++fKmbm5t33xM1Ho9X5+fna9dpveuz9f5EvvMG/flKtG3fbzqv9W4/XiPmPv/9K6ve7eN0Ol1dXFxUVb0ZR94p6P5lu/K9ptnWbf3dpit/l+8ZRW5ubmqxWLzbx8Fg0J1Ev/w+T7+zMe3ZNpa23LI/96dlF9mffOXZ09PTmu7+/vV+7/bx6OhoNR6Pu/vy7lu/XHkXf0nZNnatv1vXar1Xk1eoDQYD3jX5bh/Pzs5Wf/EXf7H22kB/Wm2xX2yT1ntQ+8Yuv6zZryJ8fn6uP//5zzvFnKOjo9VkMnnzDmKPZfpdn9cXZlzeZPNpM61XEvrVinqd3k4x5/z8vDufF6vn/YfD4ZsX1e+SV1qvj0w9teIU98t3//Lqs+VyWX/+85/r6uqq2cdeCfTw8LD+8T/+x92bvXmxtd/RR5CiUbzDzkG6FaDs9K3jfV4rYSNHR0fdC2a55mg0qr/6q7/aqY/n5+f1r//1v157kTcvyUX8rr3Wu0CrXt/naUfPIMpx6RSZKP1ewsfHx7q9va1v377VbDbr3gM5HA7rf/yP/7FTHy8uLurf/bt/171LdTwe19nZWX369Kl7Uzy6y3bwXk+/29Mv3Pbf9MvvEnVfrUt+JwjxTkleCs05f/3Xf71TH+2Ml5eX9ac//an+yT/5J/WP/tE/qh9//LEb08PDw85+eY8jAZH/OzHZ4dx+vk/nRx9+v+rd3V19+/atvnz5Un/7t39b//t//++6vr7uXq79P//n/9ypj+PxuP7ZP/tnVVXdO04/ffpU0+m06w/tSd20wG/VW4CUNpk273FMf/ULt29vb+v29rZ70f2u4/jTTz/Vf/2v/7V7D+bd3V1dXV11dsF7Rqtq7WXuVdUEErTXQbNVDHg8/e5NvzuVePfDDz/UX/7lX9bFxUWNRqN6eHiob9++1b/5N/9mpz6enJzUv/gX/6KOjo7q4uKiTk5Oajqd1uXlZZ2fn9dyuVx7Ybjf5el3Xvrl1pmUaCvvuuTF1cfHx93ffm8q8Q17/eWXX+p//a//VX/7t39bv/32W3379q1ubm7qb/5mtzeUffr0qf7lv/yX9fXr1/r999/r8fGxe8evfY93gfIOWL9c23kl434LlOaL0zMmvby81OHhYZ2entbZ2VmdnZ3V5eVl/fzzz/XDDz90L23/V//qX23sV+8XaqeB0RG/od7HVr1fNVa1q69MTImM+M4O8Pz83CnZlcGuQsLlBbm8JDev5WCS/WghRCdKJ5RWBZZInr85nxeLE5Cfn5+7/u4iHEdVhsOenZ3V6elpB4a4J8aZoIHPpuqcvm4KxhzbAkM4zMHBQecEfV69x3idnJzUxcVF/fTTT/Xzzz/XTz/9VOfn5x3o4MW9Bl0EEVeq+TORfCZZjvELjkG46BH98mLtfNH4LvLy8tK9uN7AjhfLV9UamravZBLkGonaEwBusm/+jw/5Gown/9tVaOtq9f2FzAZVvAiaOGQboe8JEPK6rfiQLxunT/SFD4mMl7UfHh7WdDpdKwh27SPX4L4kNao8+ttiA/zZVlEbANjeWmwW+js5OanValUXFxcdCLq7u+uS7a59fHl56V5eT7wiabvi9rjZlh0DaafFhQn9afWdc7H/5XLZFQSuqp+enuro6Ojd/n04gRqlu0OtqjAHthUgUAxvE3cw4O3zmaCtDCdrBmiT82yTwWCwhn6sRIOFrCKzX4nYtyXMvD99tm4cpHlbOhXL8/PzRr1uktVqVYeHh11fqbQJBLSFtmcSzwBrHbQq6UwMdnjr1Q5Mdbharerh4aFX/6q+2+p0Oq2Li4v6/Plz/fDDD3V+fl7Hx8cdSAKBO9HZkdFDK+CmgxpM5fHoFB1Op9PO2alOSaQflWRGHHjQNQmnZY8taYEei7+j7bSBxO6ElJXSrvL8/FyLxQIK/80UQgIyV40GDnmM40aL0nfb6YtB8HK5rNlsVjc3NzUej9dA2K6SCRcfJ8g7IdAGJz/6yTFZidN+H8t9Deb424VRVdXx8XGdnp7WDz/8ULe3t3V1ddX5y65CNff4+FiDwaCrPg08uSbVaLI5VfXGPxII2i48lmkj6DmZNYqSp6enrg3bpFcCNaI2kjViz4DiANlKIPkhUbrzOEAqj2s6SNmIPAB9+mhqIc9tJYhMDu5rIh87fV6v1Zaq9UretON4PK7Hx8dmYNuln+iIa1GFGf1lkmjpoGq9wjbA8O/Wg6/D766i3VdXu33k6Oiozs7OugR6fn5e4/G4G1f0mEE9g6gDlxNoAj3OtZ0aGOAj6IjK+uHhoUP2VPq7SgKaBHceR34mGG3plcCRibPFJuQxSW/7OpsqpU2C/u7v72s2m3Wg0de0zfI94IEK3UkzQb59YVtVap25z1TGd3d3nS/1GUPfw9WsWTR+zzlIj3smGyeOBLrPz88du5P9z8RFm05PT+vi4qKbIuhTgcIgDAaDjvGi4sbPW9MOCYhaOvPvGY/RAYDOtuGk7CRKBcrahG3SuwIlWbbmF+hoJo1NlRaS1Qi/U422EJWDAvd+enrqrk1ip827CgnUFIUdPhNEGrKTj/vmQLOpCt2WSE2bV1VHPRJQ+iYXV12uwoy4khJptdvtb9FCmSSty022wf9IOMxVuKLaRcbjcZ2entb5+XmdnZ11IIF+Uom22tEKuP5f62NxAnPgOjg4qOVy2en96empptNpN/c8n897B1/szeNVtY7Ofc1tgLLV35b/eQzTB/x3i8rsW4E+PT11c4AkD2zJ8Yb7urrclPTMnPn7BI1pB1nxcO5isegSqCn1PgKo25acMo5kvGgBlIyvyYxxjNdbJIVa9R2Q4k8A0T59dP8ArlWvU0mAhk1+954QM1p9tp1WVQci0bOnqmCD8NVt0juBZoWQVYPRjFemVb2iuFbwzSrHSLlVCeU9QWAEWSpWnKwP4iXI+l423EycWQGkriw4YBo4P1vXbOnXiY/J8j595FxT1XZa+kjAas2btBBfOvUmh9/WVvpYVV0C7UsZ0cfJZFKnp6c1mUzWHJT5uEzobnN+OL5VQbWSDtdKvXAsQJTFE9PptK6vr99FvRYDHle2HscMJFkxuk1UQVzP1XRrXFNayYV7Qh33TSwvLy9rc4Cmpw1QnBgY46rqAKb9xxVlVszvTf+0bAP67/7+vhaLRW+QQHs8L5hiv+Ac/8/j2gItCfbSDlzhYpu+F9Uj/tRi6N4TV9jYj2lbPsQjckjS8u632//y8rI2RYGtJJBCJ76mY979/f3a/Owm6Z1AabQVzMC2jM8D5uM3VaX5vxZ10uLB7QQO2H2pP6MY7u/g78TRqq5SHxk0s3J2MrVzp2Hb6fnbq0b7BF3O9ZyDK4VMegRlaA1oDq++5djW2Fp3boP1lGJw5oVhfUEClbqTZz6qY91lxZR6bVUqCQqznS0K1NdmPvajqD6rBfpIMtxWjVj4/r2kmf7QsheCmFkDL7DaVVar1Rql1vKNqs2LZewz+LbjVOt+SUdbHwlw+Zskf39/303/9BHa5pWmWfk7prZAENcBrOR5tpOsOInnBsqr1epNNQ3Yg83ZVaz/zB2sRfC6Gmw4E2gCN/en6nVeM8ExbTDAyjUCz8/Pa0AIMLNNes+BZpLMxEljWoa7qfr09VHCpiRrZSA4FdWKVx36Z59+5rxbolwPhu9TVWv9zr7aATbpwUk0gwXJEwOD+uhL4WKYOefZqiByZZvp5NRz9qGFetM+jAh9XDp+39WbiWZbFaZ14GP805WUE4zt2skkk9YmndqWhsNhxwr0TaAtf2n93qq0fR3/TEmg5/HelmCyrVX9plRop4N9AoBNQdI2MxgM3jya1NJRJmRXudk/rk+7qD4/AoRsr4Db1IHjmMF2+lRWqj4fMcPmosA+7QSDHkajUffoGyzOLpLVpttnMN+KE9w/wVxVvYmTCex8jPuBWCd+RI9Eaoa1JR9ahZsJsTVgNDaD9KbE6OCZSCuTjbnpRPdVrxPkOF3flY2JwLk/huYEm5UV7XBAysCTCGrb/+woWdn4UYuPLJv3aje3pRXg6Yvb0KrE/T/rz8acBum+J4WYx/UJSgAMFkcxVlRprka4ZwsgOYnn3EzLrpNGSzak9fhA1etiij7jaJ+wD7YqbIJ+InOfk2yPKxoHaY7n7+FwuEaxGkyit6yM+gjUWiZyfLEVh1zFGDCagWjpwQk6g63t11Xi09PT2rO+fefrYSEAewmisRc/yuI2Jgvn71rt8FSXqzcvXmKxVgIUaNhdHvOwmDWjUswCzGPjeOuP44l91XHaawE4Lv0v/8cYAohcOGyS3gnUAaVF1aaR2rF9jFFsKwi1UGwiZgYzEbC5bCaD+1SgXMf33IR0aEtWX6kf9yGDdMtZfc1W2214OV+xi5BEcw6Nn0bvbncLISYKNrDIOdOW8bfukX0GEO0qw+Fw7TGV1I/v1aIs0y6dcNFfJhu+97jyv9YCK6N6mIS+qN407bZgiU62gVj3w9JC/x5D68N26+BHf21Du/YRao0Eiu87Fpn6c6Wbu045SSRQz/5nOx143Q+qUObO5vN5TSaTXjFnMHitkNETgZx+b0saaXMZe2lzxh6oTCcXznd/Uy+A0z5gz5RoggBXjX3soyW58DGBSIspMwj0osz32vLh50AZ5FaVgMF6FyKfn4jCQcmSlc0mtAg6RmwMH0mgiToY3DRi/2zJtmCVTttCRPTfwZdzGQeCbt/HH6raVUqObQZ6I1fTuJv6sAl0JKjw/+mzF51kAtulb+PxeG2xgytCAkVWmrTN92E1+Cbw53NbVNG2PhOMWPDk1Ym7SDq6/Y/7uN0tH3PbW/5pPRlwtFiGBLn83/p/D9WnmFrD37EFKHpvhJG24u9ac/4cs2n8Wz5PH56fn7sdwVgtfHx8XPf39736mPbp5Okk6krUMcH+6OqV/mTlBV3qRziwc68UT/DhZ6X7PMbisTLIom0PDw9vbA1dpF1ynsVxw0VUVp5ZzPEx2OJpjmRkWvKhRURV9WbwsjMIzpvBdVNlmYjQ10jZpEQjuMHg+x6xvv97QvIw0nXy9EAb8XGuj8+A1Kq4NiWQljGkTkDUDw8PO/fP5yflZQPzXJ8rMRwsA0oGHusCVOeEbIfPJJbVH2Chj8OSkHI+ycmTFb4tPfC9qSb6kMvluaeTSurN4JP+okuejfv06dPOCTTBZQtopL4dpFu6bCVRX4N75vwY57ptVMduU9Jnu/Tx/v6+S54EYhbqsJMW4+ygz1jZF12tMtZmzEz7ZrDlePr6+PhY8/m826mM7Rjn83nvBGr90l5TiYh9NNkegzmOQe+OY9hp0sMeFwAsydIg2p8+/oje7evEBY8V8SLPN8OQecVx0k8PeEs/7ulpL8Yepqqqajab1WKxWHucZ5P0SqAO7AR0G5znkRyk3kMNrYSZgZTjU6mt5O0kNBgMOufbVZw4HCBbAd99bSFzG2CiqDQA2mz0uSlxYgjeJ7KPtIIuQcOJ0UFlExAg6HoMbMhe/MG9czOOVtKAhrUud3XY4XDYrRZ0UDWy5Xo4igEhaDyd1cnT9pdt25Q4HTg4jiX9PA/ad7GU2+jqk//n8fZJdJvHbvo9bdEVvH0vK3YDh9aWdJtktVqtPcJycHDQPd/L7lnT6bSm02n3OJYrX9O/nhdLu3dlajo9H6dwuxaLRV1dXdVwOFzb6OHh4aHm83mvmEObHCttN9wzQRO+VvW2qMmxT3aE/qcOcu9ZAKh3ePtIAsX/WLHsdnmvbzYwSCDgBWCmu9GNq+n7+/tuUReravE5rnNwcNBtfHFyclKTyaQD1GxtenZ29v9OAnVDco4pqQYr0EpJLjqP8z1bSTYDrw3QibnvRgNpaGlkNlwGO+kCXyNRWyJ8OwDXIOl4H1iON1jx37saM300gEmH4zvPZbM4K5OGjdd68abzST97PLJycmDjJw7QN4FSqeTCEc+FuUJBbOcGEQn6XGUl1eV7pu8cHBx0O7NQXU8mkzo7O9u5Aq1afxQmQWwr+JLYWgwQfWhRZj6G70xj5g45voap+E1geJMsl8uuAq2qjuo+Ozur8/Pz7gUIp6en3epXwI8fiiexLRaLtSRqGQxe5+moar3ZOgwIfT04OKjHx8e15I29z+fznWNOgmEveDItSXtbU2cG4Aluc6GhqWz3DcCQICwTt9dO9Ik5BjT39/ddv/zoCFt2tnzPbc2XltjH7u/v6+7uru7u7jo2gG0y8XOA0mQyWatS+T8JdDqdbrXV3gk0szidcQdInjhsD92XAAAgAElEQVQsx6NwO2EreOb8VFaVieo9sA66GEHfOZc0FgaQ/nJNEgOICuMw7eLk62XqplZYhFBVb7YpM73i6sXBH+lrzFXr8y2pI/THTy8/RycYvKs4B1RviZX6NJJN5/X3AKj7+/ud+zgajbrAiuOhIypbr851FeU+5KIKJxKQedpH7mTFHE9uDWb/4Dq5xH8XsT84oWFjpic5nsTvhOaqnGoPXRo0mcY1UE7WJKv6viwJ7QKMDYev89q8CcqJExoXPeArCcYdTNEDtPDz83ONx+M3lZ79kmBLsqx6fQsUdtJni83BYND1y89Xkvwy3nktgoX7AcyIua4osS/HJcYJkGJA6GTJPVos1C6C/QNkiA0AJMehBHX+3THEm95wroEI/U5GCNv3QiiS72g0qpubm86+to3jh3YiolFsQs5ziBilleFKB8lKw6U5iqpa57Ud1HwNKwbkSHswoj6JBbGivbyca7vyZOBYROBNwWkDSNYIyHM1VbX2xhMHdesBvTAONrS+wnWZwHd11arw04AdtNGJaRoDCsbMK2PRq/WbSZTr7bIriOXg4KDbON4UrpO1tw+zPvxANWOZr0ZCHwYC9A0bzGtCKbGptnWTbM2ukkHOgR8fIPn44/Nd2RCYXTUme+J5tExQ2AFAF3vPBSm7Cn61XC67cfNesU9PT3V3d9fNRzomrFarNZ1TmeSWgMQOEhjVJPciKeZahKzEGQMqUM9dbpPBYNAFa97mkgt+PNaPj49roMYAnHOwJ8bRIC/ZGBK+2SgnWBcAXJv29BlHQIWBNeNAsnOC5h6AL+IGdKvZparvr0D0O395Ow46cdWK/RrU8t3j42PNZrO6vr6u8Xi8dRx7J9DRaNQteAD94TheHeayuBV4XMGiuAyanEcwc5ntasYTwc/Pz53xY9R9dgXxtXNOgIFqVagOKEkZwLWfnp7WcDjsaCYHARyeR2+4BkaHE7jS70uHuY+erEe3/J2UjdGed/VxlY+DkNT9XBzBFF2x6w4fV2w5wU/Avr+/766xi4xGo6769OMhSVuR+LguVRQPUVP5mgnARuhrsigGkqBtaCs/K2hwmc68iwwGr7st5bscPda+hwOnV1GaPeJ4gzv0xHeMse+F/TjZ4COwJn3nzpL1wiZInDc3N2uVvO2sqrqxJIlC7fG8HxWLq9ncSo+45nuwDSYBnDE3jbhrBQpbAmVoIONCgIU9+B4+6TeJGNizsBCfa7EfxOp8G5Cvb3+FtjbI2lVyzQh69CIwM5QZZ/FbgA5jwBqCx8fHWiwW3dtxYBRaDCLtwTZsD7xzmYSdC5osH9pM/ujoqJvAZ24MlODgTjb3JD6OCWWSA5HJmGTiMt9G5UTMOUaO4/G4N+plcHNeySjPbUDJIH0CPjw/oKOquscUTCu6EpzP590rm3ggu2p94ttJtGp90dOuYqoS8eo1Bw0CNdSZX4Lr/ntpvCssxtyG7HmmTACuEkH/fnZv1/HDDkiWrv65lwGSk4opXV/TNC86d7tMDbKwhIrToBK6zPfqO9UA9ecXDxvQJKPQmputek18mUQ5h6CTbTMz4pWO9uUWFd53lx6qXPpHsOP+9/f3a5ssZEWMPc7n87q6uqqrq6uuEh0Oh3V6elqXl5d1cXFRk8mkSzYGmgYVfhOSj4fOBQz1oXBdUVXV2vSQ/ZzxIbadnJx0NCh2mK/lAiQQE7ERwP58Pu8qdGK35xlPTk66vozH467Nfdk97AHbInmyKAwfxQ5tM7TfVLcTaVXV/f193d7e1vX19VpcMvjL6ydjZlaF6/yhFagDE45F4EmKBoWRCDAKEhIJxAGzan2BiytQowTu6YUdnMsxDHzfQU4npO1VtdZPlDscDrvEnQkXamS5XK4lURYe0D4cIKtYBpN+OoG4z33FgYU25FwWeqfNRtm0CRsw6nclYqBhutZzMa25GTMABmS7JlAc1JSOabaqt3OXfMf5WS0ZABpE+P8eG/fbgCeDcisp9+2j54KcxJzg83ePlXdhoa2eHjBFTIJwcmwlf/pJzMAWPrIFnIG298W1jzEGAHe/cP75+bnm83l9+/atfvvtt7q6uqrFYlGj0aguLi66Y5mSQkeefvFiGyqfqurim3XXZw4Ue8qNNDxlBYPBdW276TPM2Xo6aTj8vjCG/tjuvGDR8TmLmaenp7VzPzJtlKupWelKYcF9DObwIVjP09PTOjs7637H7u/u7taqduIt4/by8tIBBa/RcAGC7aAzdLlJPvQ+UNCAV2iiHHPLSXG6POca8Nm8LaOqOkTlh4fdYc8NEIAxBpyZyvgfUp0RuD3HMRgM1igeBt339gpUEpDBwng87t6rt1qtajabNRPHfD5fq0S5VmuhSd8qGyf32DpxuuKHomo9U4WztVA/+gfogDZbyRMa1cvUDUYcHHYRJzlvCO15QGh/aDvG0G2A5nEi9YpAbB+9GERRWa9Wq+5l0FWvQcS27AqnTwI1rQkAy8o5xz3n0jMhcq4DTCJ3Vy25CCTfpbhcLtfG39T/Ln0k+FEtVK0vdGG8GCsqKSg9r8C9vr6uq6ur+vbtWy0Wi86mWEyyWCzWbJnAfX5+3lWJBtDWqftu33pPsBUStaeEsEeDVesWnzEj9Pz8fXMHs3esZKdP3INYS599X4NJ/MWrZPsA95wWSt9z4VNVa+N6cnJS5+fna6utSb6woOifR1Gg5anUj4+PO2rW1H9Wl6a1iQF/WAVKVid4eD9EMvd8Pn+jMM+X4RA8NA6q8PJzHCX58tFo1DlH0pccD4Iz/dG3QmMwbUgMulEJ6Pfu7q6ur6/r+vq6bm5u1p4HIwHRB64zmUzq/Py8qqprMwEBg4Fm8rsQPRYOtn0pauhxjAhqjDmE+XzeUfOgw6Ojo+68o6Oj7nzG3hUJyQBHAWmadmEawI6Uy+i5vlmBXQSq0K9O8kpK00LQ04zr/f19ZwcGf3l/VzqeO3KVbeqZCgodPjw8rM399wUJppyxBydkVxPJ6nCMq2fPf/tYwCMB3LZvoIjP0AbsKmnlvuN4eHi4RnmjY/qFnxN/eBD+7u6uixfovNUmn8vcpStIkiiU6enp6drjM9gXC5YAvbvS8SRwbztpgMAnk7PXZhjs8/fd3V3d3t7W4eH3R6RMZ3rBDkkUf2YeENAzGAzq4eGhu19VrdHDu4j9zywIejOtS5I0bUuOSCbJCc+Vo592gO1jHp6C7erqqm5vb9eKPFfi9Hlb/uhN4bpyJACaMkjKhWMJxjgiz9kwh0BwwXBN/zFfNh6Pu/KbQO2AjYEYMfeZU0JQGNcmsJHAQNwMGk47n887J6Xvrtg96K7irK/xeNydO51OO8POB4MNSuxAuwh6JvCib4DAzc3N2jOK9MsVKEZL8GDulgCEES+Xy7Xg4I+rT/+Ok3g+rqpflc39SSrYBGPjeToCsCt7Am7OReP02AL/J/gkDe3K8OHhoWazWRfYqe4Yd4BKnwST0ybYgylh0570gZ+mAQnAiP2I66RPOWG6IjZz4MVnOf+6i5hu5m+DdioK9Gr6FrqQZABVjX2bUcIfHTANFGazWdf+4+Pjuri4qJ9//rkuLi7q8PCwG1vAZ58E6rHLBW7EUBZCzefzNWBLgnNVzErg29vbOjo6qtls1tlxgobb29v6/fffa7FYdL7rnXm4B2s8qqqLw30SqIE1ffZjQOfn591ctAELjA4sHAUKc56wgOjfuvDCT/sKlW0yNp56wmf/sASawZ4gDzoiaJ2enq6tCvM8G05LQvQzpCAr04Om+1iBZbrE86tV689dfmTpPIHHlDAT8yxNd2Vc9bqtGYbueR/aZHoG4zZt5KRMYMW5GWyCBQ5qA4E+37WPLIUHjLCrytXVVccieNKd+5oSoxIFRYL8YQIQV4DcN9uKrp+fn7uFXwCNBBu7CPZjoFW1/iotAjDBD6qQ6uXu7q4LPJxLxbdcLjtWgKrDNpHzkJ5LB2RxDDb+kVdgmQ41w0NQSRbGwdoUOjaBnqhMsCuDD4M92sCxHk/8Ph8/8RjsIq4w8RHad3NzU7///ntdXV114I32MedHUskXQBOUAW35Hk/6nQEUfd7f39fV1VV3bRYBsolCH+aLcfG8u+e3l8tllzjm83nH1jH+xAziB/5JAjDNTqwmfmK/JGYDP8b28PCwY2dIpn0WSlWtP0PqMZhMJvXp06f68ccf69OnT12spEoGbFq/tlOzOvgrfmAAAgVtVs/MCe0BUJFTtoGED+1EZDSLwpfL5VqJnY+xGL3aOBwofW0Mgo6RkFCqg6vpJ46jbDe67tNP7uF5olxMlHQdyY75BgcU091Gs/xtI8ZAuLfp3ePj4y65ugrt00cSB9UHFSSrRXO8MXwMmHsR/Kuqq5L9MDbCGOO4Va9zsDg5lM3R0ffdXAAfnvfuwyYQRLkP9kFwAJVjU6124bhV63QZNujFN340xR+LF2k5ubry+whIyKBHAk1a1kkU2wFkOsi6bbZ/26JtneCatCWB31WVF+jsKtYb1exwOFwDbfgaAdDjhS1CFebiHFaaEjNcCQIiDXjoI0kXXRMfmALoy35RoSVjwtztly9f6tu3b931/QjTavW6QQE6sU1iy46T9JFixmPreddkUojvsC67SMaxqlpLWqad7+7uunNI8viaf3I9ruW1G1WvbCm2ip8Rb+/u7joaGn81Bcx1/7AEWrUeKPmQNI0uzLG7knHwp4E5+c4nKc6q9Z0p/NgMHTVlRFD+aAJ1EncAykUkOKgDI/OFnkPyKkKM3UjQgdvPkdrwXN2C/qm0+lagXq6PtFYC5jwd37uS8twMzonggOiQ4JWrOEmgT09PaytKvaChT1CiCkO36NKUtxOIARxtckBh8QL6rnrd9cW2n1WLwSN6tB/kfFefOdCcX/RiE/qHLtwmJ1CqOQdt69mUH8ie6+NvPs7t4/htz6q+JwYkXphH8DMdRzDmHl5h7ara0zTQh2y84eTix5pyDBN8eDFRH3FMgJniXlS5VNk3NzfdOHidBgl0Npt1laqpSBc1q9WqG7NPnz511CyJ2Qyex89z+DnWu4ivaXl6eqrr6+tuIwzG3Mky+0JMAvzSP1enVM85fQbI4UNcyDGxf23sUx8FMEh+IBkUBFpNJ8XAaTzfO6AaYeZqWwcXDBnHNCJycCQQG/X2dVgPGBPziWxduTh5U2HbAOg3A0jyJJhmxUk7smrgOjnP1qd/tNeAYDwed8GE4ElbATIGI8wP8H+zEq15MAdQJw2EZGV9WR9e8bqLOKFZv9gSgIP7Ms6uVrEnHiRnwRN9AohgCy3b8Tjytx/NcRXQ11YNTrFRB3oHAZKdv6dt/snxnlMncRlUpf/6w3X4iU/iO30SqCk6+47pbxbjuW/89DQHbXa7lsvvc/Snp6d1/v+w9ya7jWXZGe4iqZ6k+sjMQlX5An4lv4FnhmeeGDA88Wt45JlfwDO/gd+hDNgZlRmhlhLFRg3JO1B9m99ZcRQ6RzcHxgU3IIRCos7ZzWr+9a+19z48LFXCjl6zveG5yA/UZ12/mzSnN5w/XSwWMZlMYjweFz2z7cS+WB9tRzwHjr5I/1DJCjVP1MpcMQfYU95rdqdNM3vDHBFhs6XIzwbQujgt08DOqXvrHbLBGqBXGSS/ty7vUdStHSj04/39fTntwYULNr5Mkh2olSeHzlkZM82FkPp7F4SYUrKjew9F5OaoCAOLkzEdYCPA9wgatBYoCIMEUjLacxRt+oBIJy8i/cn5pLZRdkRUxrW9vV3JlaBY9N1FOXasoEXW1+sNmHBeI/czsxGm2TBweb6bNKIDG/s6FsSyZ9YEQGQw5pwzBtY0qg1AjuLyF5Q8lYb9fr9VHpR35TQD4zP9VDfngD4+67Vw39FRDFXOIyPTTrnw3DxHzFObRrS1WCxKDg65MEXHZ3MU7bE6YsPAeqsKB4V4fyVrhew7GqZewA62br6/1+wMoaP9fPKY2DenI7w+NKdYWAMDLeSP2oz9/f1Khb9TJnzGW1/4es+51LX8DNgh8vEGefTB6T30047ckTE1GswXIB9gVMcsum9mPW2D3mqtKdyXl5dKBMo+HO+NtCO1A8uo3MYkolr1V2d8TGXWCWidopo+btpMFdg5O9qr+0LRWCgozWyMcKAscp3xc4Utc+bIAeNuSrVt4xlc2bO3t/fNyTn5vR4/v7Ohos/+fK68NYK2Ezb4QniZiyZ0Sm4YeoM25p/fW5ZYP/rtqlF+bwWj1RkUgz6nHfx7UgEUr0CTtXWgb32eOabVya6jU4M4I/3M9DjK87yZHUJXPkLZ5jGafSISdn7ORSKsA8aWNUG30GODOUeg3kJhQOQ+QLfW5bLzHDdtRIeMkYpT8ph5qxT/Oge7XC6Lfhm41BVuOZhhjGZGkAOcdt7zzPubjjHbcI8b+cm2wAVw5DczAGBtmC/SX8vlsgQvyAHskVNjmSkwG9Ukz9vagdoB4EhZSBskowNHADyjzknVTbgHlunbvHg5os20UpvGs/kXGjAjd4+Tz0VEhXLKVACLw3hyn42uHNnkcZsG/aiR6vV65RALH6LtMvVMQVoJMvqln3Z69DmDGo87R2f8zoa4Lb1pA+migIhvHX9EVFgURxygZFcWmzXIa+t5svHBqBngMd/5ZK8265fHY0Nlqs2yCkvDnHqLg6nCnMv23xj4MbfW0bfmqg2YjVjfdJLtR0T1ggOzUYw3Ryv83H9HvQT7k72dyZFRp9P5xp5YF3JqpW0U6jQIlCwRqQFtTlP1er3yO2ob+IKutR5mvbSt89itO+QRnY5qWzVO83wZqAH4kBdAtB2jI2X6Bugg+iSvyTY6QIDZDwcprKejXuT6va06rR0oL6KkmapMKC3z5qYSnA+0ornDde+I+HbrAYbGqNCoxQqGAWvTTMXwTpye+5PRW6ZJcKAW/rqcLvMCdcqiu4wdIcgUuIHFRxpK4vNUcaDuV87lOipx89raySKMdkKsv5HmW07A1ZdtxmWA4qKnHBl6TKyfwQ+5TjvgOnrHNDQOqNtd3xTk9bTs8NWmGMwgwWCHKCIDLuunL59mfpzHjYhigOxMTJk6SrAOGgAxV+jPR7axMDesh+fZxWtea+shv8NQGhhYDqyT2YibuicqNDBxJP+RtJHnjHd637fTC9g0cvI4ARypI3Pnrhm3ARv2dGtrq1Cptm/8HzljrJm9aTI+nun/1zE8roXBafpYRjNFrFU+Mx09YB7QVRd9Oj2VAy7m+zelcFm8iPUtB+QAFotFpWiHDmLgfbixIwsbooxemRyX4vPs1WpVUcQ69MBn2tKbdU7dUWOOEAEMOUeC82HsEWvaw84lb4Vw7pF5ZOFNm6BQjlrbjNEGBTTJWDKaIxdsA5YZBIyt586gAqG0MjK3loGI6vnK3s/VxrnkohyiakeJNCtvPoat2+1+sx2Lv0GZzQYwt/47A7qcU/L6tllH/tYOw+X9GSBgPH2wBejdRtHryO8dlbMeOG5XU9exSy7gwsA3bV5HotBM5y6Xy3KIix0+f8981uUOcyTGl8Gv1wQZwR44IjXtz7ubNOYog3CYPtO3pmh9NCK/e3x8rDg3Ozl0ipPBAFHIK0DR/c4OznpiQNNkHbNd5+fWmzwv/Ov1iKgyL4BjV+w6aHPBkMfjz2YW0HL9m0egGf1Z8VA0OuQqTQtCRPUYvjyhXvhsWDEc2dhkOrTT6bTe7Ov+eEx2OKaDbPz4W1ePeREZC2PwYnn/qw1DxDqK5r111HUbWgzhykUfporzWOqKVTLoyYoW8W2BEFtUvL52sPzfRSjek9YGJPA3Ea+yRk4ksyG822yB5RCnagDjLxtsK6OVnujSFb52usxZm3X0XOSiJVNUpitxRKRcmBevrZkNGzEDBYy46bc6EIu88ze5n03X0fkrU7nORRq0mebMINP6aqfH+NAPAgQb7beYLn7vCK5pYxw+aCLbRoIO2BjfRuLiGPcBoJQLbSJeb1U5OjoqJ8mxvpPJpMKC2FYx/+Rr2xxXyFgywHHLNoGUCraKPCifZV+5o1bbNTNGfkdmkjILhk2uKzTK7UMnEdlIGPlaEfmcnYKrUY0kI9YLk1FsFlIEPhsvv9f9qos22o6X5kgsR1/83s4wLyoNIIGAeMEcjSFsKIKjXxtcR9xNmvuZqSgrYDbAmdrO9DGOzwY25+gYl/O7WXHsfOnLR7d4YDjqaH9HEj45i3nHELImPhrOkYLXLq+Bo9q8z9XraBq2bcv5I8YZUS2U8ro4HWBdQq7NeOzt7VXkLkc0zJFz2XW6W/ezJmODrsRomglwtGAHCrXJWnqsBrG8I0dVOE+K6iKiUKMR31KSdtrOpTdpvO/5+fmbdI1ZCmzBYDCoXOnV6/UK6HZ0yjm9EVG2GnqM/L3H0Ov1SoGjZZN+Zsasjbz6mW850xwgGIjmfZushdeBftIvQKN3AZAOyMDX+us+fq+13sbyPYrEQoXzdA7N92Nmgwl9wCSB/BiUaUbnNI0uMzKsc3JNmseUnUZG13Xvyt87ekUYTK9l+sCfn8/npcowl3k35enrWqaXWZc8V5kdoNkRASoi1nm2XKTCGjIGJ/BtfE2H2ZF/BNnT7CBy1JeLFDxW6ENfoGCqtS7qw2DBOCCfGB07LtPiZlaaNowloDSjaSKmOjCa1zXPjaMdy6cjPgATn6/T6exAP6KLPiKT51n2DTyZF/4WyhgHQj/oJ2OBnUA3OdHn4eGh5NRMgZv2Ze6YBwx007ZarY9R5D2r1arIHOPe2tr65hJ6aFhkz46cauLlclmp2McWPz8/R7/fj36/Xzm1yEAFsOGWwUbTxjoZfPI9gNLMAA6f9wMMWGfrCrJr28ke4ePj4zg+Po7hcFiZK9b/rRRfZpfq2oeO8rNTQdEcpZhKNTUJunellcNvO1AWGOPivOru7m5FkbJTY0LqDH+T5hxJnYDwPlO0/p1pFud+62hPR482NlZ2nwHKfNsg5gj3veYIlOMDHx8fKw6xDiTknzP/GHCcg7et5FxfRJVG8X5Zj9+Oky/63maMGJDcbz5TF8GY/jo4OCh3DxLVZKYB584au3qSOconnhAV2zi0jVzQi3z8osdq+g3DCJDN7E0drWUZY1wc1o0zycDGUYbf7fVrS8U7kkYeyN1mapz+TiaT6HQ65fQoimx8kL9ZMdbal1Sje/7sarWqHApiBgWZ/YgDxT4iF/SDMRF95huxcvGmAaxljrV8fHyM+/v7co5vtuVm+BiHbb6j0DbAPbOW/AzbwVdEVIrGmPeDg4MiVw5A6J/ns9frleMZDw8PK1ef4WvQfQ6PcMsplrfahxyoFYb8BPSUy6ARNpcOZ4Pl8wvtOI2GclVbXVRnNIFC8M73JiE3jCTPzo13I0QR6431RMjQBhZsHxpvlP7y8vINzWZh5vkYjBwBfSSvxDOJ9mezWfm5cxzZiZr6NZ22tbVV7kuEcnOlZ87DoDget2k2ItUMypq2TBWZas1RiyNgomSuVUIBfUpNxLqIjijea8t6MpfOH3kuDS7I8bWJ0pA1TrXK4895tJzPMlvi/2cdZd3Rz5eXlwKUfCmEgWCe/wye2jhQ53Md9fEM5ht7gYHnvVSYdjqdClXvcTL+TK3zc+dZDYJz4GDmqmmzk4iICmvDmIhIHX3m03V8y4yrum0fp9Np3N3dlRPH5vN5uagiIr4Jhmy7eQ62AVDYZpz+vL8nusz7xNHFw8PDSqSYq9n9TOYMAOxTviKijHV3d7dyF2qm/D3+t1prB5qjhVwWbQca8W2EGrE+T9cVvA7VGQzGzFQFQlPnQO1YidJ4VtOW80GeXEdo7iu5C77oK3TLYDAo14RxXyhUmOcI9GhE5sIV0yams1j0tkaJaIlcjxF8rgr23CyXy28iVw4B2N/f/2YeM0pnze24jPj8r6nbtkAhK6yr9ExRGXhBK7PmpluNfB29AgRxor6/1ZGtc5Q4UOe62jqWHAXWGRK+5/OuHM0H4DMvb+XwHdVCi7pK1XpWx6pkmrhJ47m2LZZ3U9Z8nrmOiMoFF8wDc0Y/DQLz9g7mBDnB1pgq9Xy3AXlu1m0XzJluhNnCNhgQ3N7exu3tbbnOy/NnnR2NRkWfeOfh4WFxRgAhbJzpcGwqzrNNlO1nMX8023nL8mKxKBXD9NV+x0DCThc59XzlKDznrC2bADIXyb3VPnSUnzc14+kRVDsaOuUjt1Biro/KhhWhMC1o55lzh/TLyN6KW1e12qSZauNdRiNGrb3e+jzbiPVxfq6Wg3YhsuLuQlM/FqBc5OGo02OntXGgFuaXl5di8JlbKEfnuxAoU0IYYZqpNvoKxWlnhBLaKEes18rOs65StekYDX4wvDiMXCFtoOAxEvkDGLx9w7c6cPl5vgwAOe71qpvQmT8cg+9ebNoALvP5/E0Hynw7rULEkwunzAY5rYLTtdFxvtxG6S32xmCqDVDABmBgs+G1nDjqhWZF79BdU4U5Z+biHTsHmB+nLQwsnPJxKqWN3TFFDDhhvrC3/j/ObDabxf39fbmpZTweF2DLHEHFOjLjGWZ6XHiFXmQHAhMBQGza0AE/LzNuli3WE4eOfDpX7Cpg1sCg1ikWfBJrZmakDgi5X7+ZA6XTLIY7706gUObiTeflakomF0OS9+0YcdlBZ+rJBiIiGk1AblkJeSbvtGPNEQxRNALp05mgNZ3P5PMGG5n65V1eA+aMMWZKq0lzlI3RZ11QEpwNawwq9LqySXmxWJRDvolquSwdlMf4cNIGIfQ9R6EeX5s8b6b9DBgcgToqRSFRPN+OwTgMZPgb373Il9FyNlTZgbxVTfhe63a7cXBwUBwo+R0364ifn4GZc10YZ+QP58vvnN82+nfDmfB3POcjESiyh8xBx5qpwbagh45qzOw40qljR2ysM2OWAVCd/WHsbZujf0ebvI9nMgeAdqLKu7u7UjHMJe9Ok7CWOBbbrlx5Tl6QZ2ALc51KG0bI+phB0FvykISlwFkAACAASURBVB0f/QLYez3eAjEGWZ5Hv9d1JQBef32vfegsXNNvDqmNAjOycAjtXBMl8kSa3viKAPBV59zc/HOH5W0dqPdsslA8x8Us/nJej/9j2HgOSXcDBp6VKU/Pp/vmz9sAtEX1FiCE0qXuRmp2QqabWTuiLdAhTgWWwQ7IBoC+2JjnHEwGBm0Ulmf52Tg/G3jn+VA+HKj7axl2TszGxRGb5Zw+ARyonjVd3Max8DekCXCkmbbN82EHRmQGKGKLjeeDecqgFKeEnOZ3Zv3w37ZlS+z8XOHKc2BGGBd70/0u69ze3l45vpJx4zhwPo5o9vb2SoU21K7p97rIv60TzfQ547P8mnJknM6/m563bGd7EVE9MYx+8x7AkQs5cby8EwfatMGWGBCxZgakfiayh33yJdhmS1wNbFlj7gykzHLBJuUAhD4i99+zOR/axmKjYcdhR5cnyvSYow+jR/PvNuLO0fhZGTl6oEanH3GgRDxWhoy0s4HodDoFHVGpyPjpvzcgY9Cda7VB91gyNW6n6ciuaTNio+KQPWVGnXbuVkQXR0Htmz5hDhBeF5o5KjBlk6NOj5soqI0DteO3I6wzUFmJoXcsY5bdHNH5bx15mfb23PL+TG83HR9/jwOlUAIwk2kyDLD3GbI1xLloZMI6l/UA+fHa+O9MkTEPdQ686Tq60jfvAc/RDGDA0aDzeV43p01M8Zqa5HNcOE1hi1My9MHOqS0Y4tl2TpZ5O1HGZ+COHtc5NfpCv50S8yUP1kNsC/PnqJQK87ayShWt2S+anaXpdTM6AIXsUH3CGA2baOeZt6KZZckOlDl7DyS0jkAztZn3C9lZ5eIPEHhWUJon1s7lLUU2gnKzwrZF9jgDK4NzH3WTbGUFqfLlnGWdYfLceDzZ8Jj+sJAzRtBUk2aajr6gfI4M+dfRv//eFFO3263QoY5kUHbTzxgmGwWvUwZDuQ/vtSyLjpoYu4GAHaGptLxW3i7hVgemut313mUQLb/z+uUopuk69nq96Pf7MZ1OKzUGdmBZhnC0ll/33y1Hoo5I+Rs+A/vg4qM6makb73tj3N/fL/UCdWe48kxkzo6EfvE3ZpFssPmsDTQsBKkWMyikJ2wDsg63Ae6sm89zpc+2O8gxzI91p44qd19IIw2HwxgOh9Hv9wsAo5K6Diy6TiDT2U1bp/O6Tcg6YNtnO8uzYfHsuL3N0f+3zPF833QEc8H5wXXRt3UC/X8PKHxoZ7qNjQ/5Na3D4hnBmCYzjWZHkh2MFTJHoEbv9MuCxlebRgSKktv4O8fp6i2PhQgz7x3jM14MP9uRAmiQuUQQ8iklzuO0iUBxXiBtxmykbuUzgEDYMMIGKTgJU/s2mI6E6vaK8o4MVBwhtnGgGEb6ARpFKaiydDQNJWQq1tWX2ThmRsJzhKKyvtYNU3KOgNoY3V6vF4PBIMbjcYWiyqCN5yInGH8DszzfXnvLsVMszonhRA2oDaozBdkWJHDEHIVBsETOrSM35Aafnl7v08R5sG2BfL9ZGIOFXIEMoGetfISeUwI5Mm46RuYH8A51CtCzvHpP62KxiMFgUPKeOZdp2ex2u2VfJIxFtifMnauw7Ty9VaYtRQ3IZz6ZIwdDtqNOg02n0+Iwp9Np+b9p6wzYIqrpRor0vJ0lf5518Hq8Z29aH+VnwXPex1Eoi2LHgzCz0FZIRymm0vxz3k9jgM7BWPmzEDc1vHzORmixWFSQCQLsU0BwnhxqzZizImZ61CgnRwzb29vR7/crBthONlfQtTG+0ECOnv1+jIYjrxx5RFT39YGY8++deyL/hBFyRSGy4PmmZeq0SbPC0pec51ssFqVaOgMG5MrG03kUO1anNKBRkRNXoefcYXYobdiSbrdbDKKpuDxPjqRZYxerOZeYG/qLg0LOszHF2Bo8eu5MobVhS3q9XhweHsbDw0M8Pz8X2pXxG8SxFj75DDo0g5dM3VtubdQjXnWFSnoftgB49p51+sO2rqYNXWNeSX9ErC927vVerx6MWOcUh8NhBaTTZ1e58zNHlUST0+m0gG/ssu20i4wc3SMvbZmE2WxW/t5AzcGKAyWvo2+lccRpIJjXzmttwEr+n/fSB4P9JqD9Qw7UnWWAueoQB+cKzbu7u7i7uyul1nmrBAKco0wG79M38uXDCGCOQCPaVcXZoWXaGaf88vJSjA+KFfEqtJPJpMKzb21tVQ4kcLMwGOWR58S423k5n+fS/jZGieiIuWEtrRj8DiFG4exEHV1YeFkXgxnQM4cTeIMzTseK6qgWQ9fGgVqG+NeFMgZrVEv3+/0YDodxcnJSQfwcdwb94+pozw/Rw3g8LtuUrOTeVmHq8SPRZ8Q6r5S3SeUqebMjk8mkyLDz9BiSXHtgo2uwhcxOJpMydu8dZr7trP3VRlb7/X4MBoNCbdZto8PeYPic82W9yaNlsGjAx89Zqwz6OIcWdoGtHsgLTm84HLZOHUWsT62az+exv79f5JS+z2azoru8s9/vx3w+j4eHhxiNRjGfz2MymVT2apLHPTg4qKRaWGcCg6zvPk7VDjRTxO81HCgAx+uXdTqnQ+g/835wcBBHR0cVm5gZE6cG7TN4hncDuCaChj17j6r+0HVmzlfZeORcKMK9XC4rex6Xy2Wp0jR/XVecYVTHRAwGg+j1ekVxQEKeUNNibRqGOiJKJIRjyUKEI4ISWywWxdhCrbgc3OMy2gURQlHYANkZ5yS/941+9K5MG0oMDfOJ8XR+y0DJ85xzXJnahTo8PDwsURPO3xflmgL1s9o6UChFFNRRPZGyDSlGl/72+/04PT2Ns7OzGA6HJcrL0YtpTBD93d1d3N7exmg0KvtDGZ8pW55FY77aRtk4T76cw2VOHd2ji+ghn8dB5asHbUhyzhqnxTgwfDn36oNG2oC9iCg6Px6Py9nQ9MvpDgPt09PTCssAeADYsB5ZdpFpAydv5zHlmcEn7z44OIh+v9/KgZoGpkBmOBxW0kTYTOxqxGsF/d3dXYxGoxiNRjEej2M0GpVDFbi9BHtJBM3pWmdnZ+V9RPbozmQyKQCBtUYO0N02QIiitRxl8gyzYravzLHTW5a5LHu5DsNRLo4TYG5dyT4n+6S61tqB2qBHfHvsG2jVxg9j0+m8JpJPTk7i4eEhJpNJKUs2revJNaViRbFxzkbH1Z0faeQ6ybPYyHrS6Sc0Jsax3+9XcqF1lJpzvyDC2WxWjISdFCjY0T/IHoPURmER5l6vV4QEZwpoYLwWSMbqaITn8TcWbOcNTY8gNxgx3+WXqWFyrW0p3OVyWYpreJ6dqGXV7yPHdXx8HOfn53F2dlaqk1k7/q2jq1kLFHdnZ6c40eVyWQFDnivneps2DIKpcPQTI0QzvRwRJXq8v7+P8Xgc4/G45A0zIDYbg1EzG4Sj8XVcLnBjXkyDtxljPsyfSAY7g064ZsCHrQOYTAGaEXIUHlG9lqzX61XAhdkgPwt6mfwit8c0aRlMu+LVNvTp6SnG43FhppbLZYzH47i+vo6rq6u4vr4uJxLd3NzE/f19pWIWank4HMbx8XGcnZ0VMPH8/Fy5vQWdNKCmfzAfnrMm64h+sRa28U655VqLfr9fdNepihwARFT3uZrR4zM5crZvcl951m9O4aKoGM2IdRRqhUMgvE3F6NgVVHUVfM6x2HCaDgTJOuQ3193WINH8PBfamPahGg3kxlgRBGg6oy7nopxbgHYDELiKkJ9hrLKR4MvXEjVZR57Fnjl+nh1oxLr6mL4Z6ERUi6FwsI5EiNw49u/5+bmyn80GwzLjE1PaFi/gQFerVWW/Fw4UOQPde43JA93c3JT1raN0WEfWMudn+CwymaNcK6pRfpuWS/RxMqbd0NPMNtBH08+5CChiHaXxvUGxHZFZAwMFZDZXPDdtjmApICJKYl1hFnAQOLLBYFBuJbGjzU7T+UfPAZEY8mEbF1HN8SMnMFJNW3YkrM/T01Pp++7ubglWiHYXi0Xc398XtoMUGceFwu6xltCnzilmkJ/XGRkz0GeuDQCbjBEgFVG93NxOivl0npR5x966/sPAGt3NNso65+069IMAgvfzLPT6N3OgGENvJM75MjsJCzcKjsI6mevqPSe5XQRglGJqM78b5+ko6D0U4WaqlgVh7LwPYeKUmoioGHua5yIjoRyFOvqDtrCSZxoMTp+vtnklMwSM1YgOABIRJcfb6/XKWuVKVT/b8uJI1gYAxA6ydQUh8oLxQPGn02krBwrdhXNCNhaLRXGiW1tbFbkzeLu/v//G0Tk3k6NQ+mY07AIyz5EdpinPjwA+R3w590/fcGReK/rCYd1QzR6f+5tZFMbgfb5v0fcuvsr5rfea37G/v1+h7jJjkSPdzDw4PcHY+Ncgl585xZL3OjuQcASMTWgzRo8jono+OBF3RBR2yvbS80P0iw5b9rAj0NM+v9yV6Lwfm7KzsxPT6bTYdCqBzUQ2aXa6zCm7AeqcnW2Gzw63TtuOAngcdJmpw5bA0OCY6RNzhr/Aaf9mDrTX6xU6i6gCx4EQMBh79Dph4/scUtvhZdrPzsS8txFWzi3lqKHpOD0WnAsTHLG+U+/h4aH8n2IU5zlzhOIowA62LvdnMMD3Bh42XG3yLcwlkS1C6IpKH8LtSIT1wNmBAllr1tVGy9WrNjQ2WnZyFBtxWsx0Oo2Hh4e4vb39xgG81aC36DOAKyNMFDlTQRHrMvjsJLMjscNxpEs/7CAt94zfesDaNB1jZn74e+eSeC4y5LQD+URHGNmBGgDxb6b1GQ/6mWlV57JdE9CkWS/QP+aRPnj+WFcYFvSQ8549PzzHEQdzQN4RYGGmwn3ge2/tchqmSfO8OboH4Fh/mD/YGnLEXmOKp7xOvMPXfJn+99hs67vdbtldwGfz9qsm4+v3+2VOHRmzjmZsPAcAWrNjrJlBbET1cBT7oOxfLMvIKTIKUwZQ+U0j0MFgUPIScOqugsuKm5XQRsi5CCtxrkj1wto5GfGjDEbg/l1TNAhiyaXb2VDy2TrDZ2qZzyAwps7yXGAIyNsZUaNARKA+fYbIsW3j+Z1OpyAx00l2zDlHQX4GxbQTzGgc52XWwuwBf4dSDofDODo6iuFwWN51d3cX19fXjcHQy8tL3N3dFYNCFJ1ZC8CC5cnIus45GtEjF3VG1etPs4za2fJcA8b3GiCBSlgbSxyCmSBThI4QHTFnnapjSeyA8t9mAGV9zECt6RjZ+5cjixzt2hDa0eNAaQabnhvbI+bOW1QAH3XBAe/NbEWTZgOfHUNElHwqus6eWDt+U+kRURxBZuCwL9gPH7TPszLgdOTH8Z3eR9p0jBykgCN2gZMLM702+XtHlf69QR4ptSyPXhfGhC2CyeNZthPfa60j0KOjo4iISujvg+IZrIUaYc8K6kFbIS0M/lyeDBp/ZwTn3EYbmgFwQIRpxIww4uCc5Lczoh/0ycjKfa4bL0oIysu3uPAeV7E6sm0zTgCQo0hHXI6SWAvm03s+8xfPt7PMzhNDbgNLf46OjuLw8DAODg7Kdqebm5u4vLxsHYGa1iJ3RBTjNQAYZIYj4vvn1Br8ZJkGJJkN8RrzvYt+UNwm7eXlJW5vbytbFsx04FSZXzv/3F/Lt39vx2k2xRGZ6VHru/OfyBg1D03XcbFYxOXlZamg5d5aFwpmdsN0MfNu2TRN6LnxmvIv8oBNoSqVxnjzTSZ+33sNXTRbZlak1+t9c+cqtskghbFzwQPrnfUyVy577Xmm30f0R4HcYrEoFHBT5svAMrOOyBmfs/0262D9dArPz2AOM3AwYHbky/PZCubggPd/r7V2oCcnJ2WgdTkG50FMVzFpmc6K+LYKzrkzJscUnxcN4Xjrd44SmjSQEvw3zhMD5f2TppZYVBBaRsSeB1Ms2Rhh8H1IeN43yO8xSqYhmzT6zXrt7+8XgYKqYY3pL6jNBtLrZpq9jqbPn/N8OwIdDAZlqwsg5OHhIa6uruLr168lJ/1eI3KZTCZlWwHrh9w6koQlQEHr5NdGx47H4KPOydgZ8b5snAEmdXP0Vnt5eYmrq6uYz+el4tIFIaYkebeNkR2jmRHTWzauOQURERVWxCkH5srVs+SxvZ/4vfb8/BwXFxdlDyRbvNiTifySr3NUn400/c0FTaxHnivLRganZhZcVYwuOlh4r0GXUoGPU+v3+6WoaTgcFroduXOE6apTv5dxud85vfX4+FjZXuR1M33tVB1HAbYBfAaQ/pnljD7yrxka+wHrselWAE4OCGA+kGHsDc/CgfJZp86+11pTuIeHhxXBobOmGzFAGZFGrFFwnrSIb+nWbORy7gglf4u6ZcLf47Hder3Xk086nU4RSGgMV4o6d8RE25B4gZgnPoeSeg8tDszFEmze975BhNsbudsW2NA6nfURZ57j7KTsSL11wNWemX2oYwGMCm3sjOLZQ7u/v19AzGg0isvLy/j69WtjChcH4guuyYc5Isp0mVMBGFj65yiLz2ZHytgN2vidHaOjTUc1jvjfa09PT/H169eSp/MBJT6NJyIq0YKjHVfQuwo1588Yo9fW1KUPHsChONVA7m40GhUKskkDJFC05/3CyCR64wiNcToKNeitkxeem/fAGmjY3ti+OQ/NLoOm67i1tRXHx8cxmUzi7u4uIqLcjnR8fByz2Sw6nU7ZqkZUyOXZPu4u72rIlbjYj8wQOfftFAvPgb4FTB8eHsbx8XFjBwqTZ6fIXDnPnM9qzv2jj4BdbH4GeLaxTg0iH7bNPl2K9UeeftMIFAfqPU6dzvpIM6om+XmORBxZ1uWMaCxuzrPUIRejTfPePIfJbepctra24vT0tFRjUXxgh8ozc+Lb44XnR8kyMPCcQofaEPmWDZ7hKB+lpX9tHSgGkZyI15NiC/pnI5SdDgbJBoR1QMhtfHO+inVFsTlkgYjF0WcbB8oa5UOoUdIMCJAtR2OuGmS+DQY9j6Y7vTWgLj/lvwX92wA0bU9PT/Hrr7+WaMRUrg9FpzFmg9FslGiZMTDrkCNMwN5gMChzCw14cHBQ1nk6nZZN/h9xoBSfANzoF1XEsF92BjbYrAHrgS4joza4Lvwz0IhY58jr2KhOpxMPDw8xHo8b6+P29nacnJwUNoHq/m73tebk/Py8pI62t19v3KFADsfkXQvepoJDNePBGJ6enir7pB15Iu8EH+QHccJnZ2dxdnbW2IEuFouYTqeVCBgHyuldzDf6b8BHczSJbLN2lmWv21vbWtjzPRgM4uTkJPb29oq9IO3zXvuQA4VOQPCMUohIs7G1QINiaJkuwiAb+UZUt5gQ9dhg23Fa+aE6mrStra349OlTERiimPv7+3KyB8qLEmIkPYbn5+cCKCwwOcqOqF5IjkHirNg6NEZkxNioUm0bgfJ578lk/vw+R5j57x15ZcDD75yfsvMkGgTd+rg8mIPRaBRfv36NL1++xNXVVSuaGsUxQgfZA0S40QIDizFyhJHpaUcwOQLNxtcRuo351tZWkR1+bsfQpD0/P8fnz5+LHjBWxoHR5/0YQ+Yf4MY8kXPHQL3FGNgBg+A5otHRJ1XUrOV0Oo2rq6u4uroqzui9tlgs4uLiorKdoNfrlRO7GBMUHGvmCNJyh73K1cYGQOizi/28ho54mT/kmSjy4eGhcQS6vb0dP/74Y/z666+xWq3KYQkvLy9xcHAQP/30UwHIu7u7MRwOS37fKQCzLT4mNbMqprcBILAH0OHIF3Smt3f0+/344Ycf4uzsrNYu1LXlchmj0agADwAmjt/gb7lcxmAwKOtVl5e33a8DqAD4XKWO/4G25TSm09PT2NvbKzsrvH/4eymV1gcp7O3tlWOgfEwfeQ0cDovnHFKdMXJe0PSLDbInh6jTg+Izfg9fRARtcqBnZ2cxGAwK5z+bzeLm5iYiopK/8WEE3n9k5OMCh7p8LGNByU0FO1Fu4Tf9wYLf39+3Mr4GHTgwC2tE1bF6fmleK+8JZYwGRqynn8GYofowgqDf8XgcX79+jT//+c/x9evXuL+/b7yOEa975jAQdqKU/Jv2c/UmFJwdpsfk8dc50AymcnqD+cTwoqTsj246RhwocmImIIM75IfN+T6KDWNjQ5NBrUGsv7a2tiprx1zlsU4mk0LF//rrr40d6HK5LIcDmHHa3t4ulDXzSPqF37suwBFNZoQiqsVztAwWmAdqGHgODgcgy9F6bR3o+fl57O/vl+P5Hh8f4+DgIC4uLuLm5iZOT0+LAz0+Pq6cLW660RQ7zbUXZrhwmHnfLHPB33luoJaHw2HjfP1yuYz7+/vodrtljOPxuDi5fIwpfXVKAx2LqN9jm5kgnLEBICxfv9+Po6Oj+PTpU3z69ClOT0+LnuLbAJTfAwkfOkx+f3+/bDPodDolCiJHyMkd3mdnxGOjk6nNTOny/+xIcY75GfSR/AehfhsHenR0FJ1Op1DVk8kkrq+vSxUo4ACEvbOzUyneMIXp/GUel5WTMdZR2o5QEViACgrbNgLN0bwNEwpU1+9c4YjT57M2xBHfbj/CmTIunx3qiGU6ncbl5WV8/vw5Pn/+HJeXlzGdThuPLyIqqJy5QnH8fqISDAjUqgGdHYrnjXFaeXO+jYIvnCPyg3zw3rZg7/n5Ob58+VKq4HFYpiSRw/l8Xsm/oydmM/JaMT4fAuKGA/UpWRkw4dRHo1GJPtvmssn3mUZlPh8eHkqBC8zF4eFhGVdd0Rky6/VlDbOBNvXrtIfnbWtrqwQNHOjeBuzBenHu8mLxesLQdDqNg4OD+Pz5c/z0008F2HPUJJXJ3J7ii7hZG1IU2Ckfb+hLCLBTyAvri/Pk0APnQjMb8946chgDN7I8PDyU/uNEqbL2wRDYI6+D7Sey5pQan8221MWeJycn8enTp/jhhx+Kzd/Z2YnBYFDG+l6lcev7QI06j46OSsn0bDYr59uC5H0ljvMHOQyvo2r9r40YP880sWlHBkzhT1aU77Vut1tKtIfDYdnIf3V1FV++fCmGnAiTUz/I2XphV6tVMSx2lDmvhFOy863rF3OwXC5jNpvFaDSKm5ubuLu7K8LZdIwIJVGsDQVrxDjsNKFrDXoMfJ6fn4sjraPWnTvLuV4ouPl8HtfX1/HnP/85fv7557i4uIj7+/vKloz3GusAdfjw8FDey2HaUFPIow+F91FnllXnNO00WRvLMdE1c+ncDY4Siow5NOJ+ry0Wi7i9va3UJPicUFfc4ohMY0eswVmm2B11Y5gy6HUuNDNG/tx4PI6Li4u4uLiIy8vLuL6+bsWWMHcvLy8xmUxiMpnEarUqlezb29uVbRXdbjeGw2FFZlkfPzNHaMi2oxXbIFOFdhzk96bTaTlGz0Dxvba1tRXn5+fx6dOnODk5Kcf2zWazuLi4iJ9//jlOT0/L78nPnZ+fV3Ke1Bw4PYHD91GPACfAa6a/zahkxgFb8Pj4WCLvJm25XBZnyXum02k5h9n3SmNPAYREoqxDdtqeZ4Mcr7npalIOx8fHcXp6GsfHx4Uy3tp6vZXJtuk3jUDpFGEwx0xx/qQjmG63W3GiEWsK1rkGR5BZyPN7iRbyMXIuoY+o3lXaxoFGRNnMD2qbTCbx5cuX+OWXX+Lr16+l+s2UJegXI8WiYyDtKG2gIr6Npg0q+D3jJ6oajUZxfX0d19fXMRqNWkUuzCfOZXt7u9BgzKVzohglokxTPDQLKsjXkaj/HsrWV5tRbfz09BRXV1fx+fPn+N///d/45Zdf4vb2tsJiNB0jeUaqlDEao9Eojo6OKsUgdhSm4L3OWWZxqAaCnjNoPkeXIG2AxXK5rOznzTTx99pq9brFxyf75FwkDZBrY2pWw/u6WSv6V0dNM0YzC3kLB3T4zc1N5bDz+/v7VmwJ0QggnegOW4BRzJX+VK3mtXHfnQ4yIOD5ZnwM2l3lOR6P4+7uroDZTqfT6nKHiNfrz3744Yf46aef4vT0tNydeXNzEz///HP0+/04Pz+P8/PzyvV6HAhvXSPKctW5WQoHQWwZw17VBS0u2AJozGazEjQ0aavVqlDO2AGofV/9h5yORqOiE4zVzwLg2GHaPvFF303dkoIcDocxHA6LQ0VWAGR87nugvXUE6glFGXEGdXQQE+zSeEc/uVKxLsdkx2IEz7Ot/BHroiGUuuneQZqRSq/Xi9/97nfx13/913FxcRFXV1eFrmaLgEv5GTP5LDs/j8vRRkb2VlLm1FHS/f193NzcxM3NTbkyywr0XsNgvry8xHQ6jU6nU6JQKBojUkfW/C03JFjpiDxzAYYpJZQboWU/Gaj75uYmPn/+HP/zP/8Tv/zyS1xeXpbjEinaaLqG+Qxfzrbt9/txfHxc2T9oRJ4riu04nPe0kckROUaLqlTACldEEcGhsMvlsuQmm7blclmJZjEqKLyBGkbPFJyL0nLUbAeanYbnAafv80qdg5pMJnF5eVkcZ9sj7qwrBiFsfYDWd6qE8ZOfRAdzCoiopC6isb5mYGOw5evrbm5uSmWro9cmY+x2Xws0f/e738Uf/vCH+PXXX2MymcR0Oo0vX77E7u5uHB0dlduBfvrppyLLP/zwQ6xW69tWyA0jF6TdfIeyK6gzS+aGneNvYDIeHx8rZ/Q2GSNpFPrEs6g5wJ4Srdr2RUShc/NaeQ2ZSwOkiCiFQxQr4jhJH/X7/dKfwWBQDnN5717XDzlQ5woccXY6nRgOh2USUCIEMCNZlxjj7DLXbQPmiCDTFQiAczwRUT7bJgLFSCCgZ2dn8bvf/S7+6q/+Kr5+/Rp3d3clskaZMe4sXt1cOWeSE/68NwMJnsXPfXEulcHkFNo4UJAkRg4l6XQ6MRgMCo3CXDI+F31xAwxj9tYN7yG0YScxz3F9JOzJiVxcXMQvv/wSFxcX5ZQd+kKVXNMxeqM3yBZDRSTDZny+OFfUUSb9p0oQY86YPE4cEkYL50gl92QyKUVLGCSe48MAmjbLNgwIOsm6RUTFiTIOPmvU7lSD5zLLYXQazQAAIABJREFUaY7IvGc6Yq139/f35co0gF7bhlz7b5+fnyuUIEV/+bKLfr9fIhWanXKmBvPcm10wCwF4cR4SFoetO20iUFiso6Oj+PHHH+PHH3+M0WhU3vHly5f405/+FD/++GMcHR0VliwiSj4PMMahDGzzINr0sX1E2q7+t+2KiPJuKtU7nU4B9eh6m+aUEawPzpgv3kMQws9haQyQ0DeAKO9gbDm15z32Th0xL7BBsGNEqN9bx04bx9LpdC4j4n9azdr/nfb/rFarT+99aDPG//NtM8a/tM0Y/8+3zRj/0v7/OsZWDnTTNm3TNm3TNm3TXlu7O7A2bdM2bdM2bdM2LSI2DnTTNm3TNm3TNu1DbeNAN23TNm3TNm3TPtA2DnTTNm3TNm3TNu0DbeNAN23TNm3TNm3TPtA2DnTTNm3TNm3TNu0DbeNAN23TNm3TNm3TPtA2DnTTNm3TNm3TNu0DbeNAN23TNm3TNm3TPtA2DnTTNm3TNm3TNu0DbeNAN23TNm3TNm3TPtA2DnTTNm3TNm3TNu0DrdV1ZmdnZ6s//vGPEbG+89LXGrn5WiBfE+R/88/c8gXb+R7Gt+7R5D44rjTi6psvX77E/f39u/dE9fv91enp6Tf3kOYrkLjyyXfRtR1PHtdb4+Tnvm6KL99r+OXLl7i7u3t3jLu7uytf0+PrsOr6/tb1Wk2u3WpzNZev1HK/vBaj0Sjm8/m7Dx0Oh6uzs7PK9Xlv9cnjz//mr/f6/9b/v7e+XL/EPZSXl5cxHo/fHePh4eHq06dPtffI+kJo5PUjY8nXgOUx5DtS/Tlfded7HSMi7u7uYjqdNtLHs7OzMje+UiyvG99/b2zf09HvtbfmY/WXS7199y06+pdrAt990f7+/soXvHMdXZ1983y7H03GWyfXb42vzr7yZZt3f3/faB2Pj49Xv//978vVY74/lrmznvquVn/V/eytNa+zq74qk399LR+/9zr+5QrA2jG2cqC///3v4z/+4z+i1+vF/f19/Prrr3FxcRGj0ajcz+lORkTl0t58Bx0/q1u8iKgsHndXcqGu7+Kcz+fx+PgY0+k0ZrNZ7OzsxKdPn+IPf/hDnJ+fx87OTvz93/99ozGenp7GP/zDP8TT01NMp9PyzE6nUy5k5VJW7nv02OzUvDgsoA0AX9n4IVCMlcvDuTPw8PAwzs7O4uTkpNw0v7u7G3/3d3/XaIzD4TD+5m/+ptxVyT2OXLiLA8P41Tlat3w5Mb9/67Ji3yuJkY+IYjy409F3w06n0xiPx/Gv//qvjcZ4fn4e//RP/xQ3NzdxdXUVT09P5V5A7gil+T2Mw3eEMidvXZKcnUO+V5Mxe42R3/l8Htvb23F6ehpnZ2cREfGP//iPjcf4L//yL+Vuz/F4HDc3N3F3dxcvLy+VexC595B7Mi2ndePxOlp+PQZ0bz6fF51EfrmrEZ3Z2dkpc9Dr9eLf/u3fGo3x9PQ0/vmf/zl2d3fj8fGxXF59f39f7rv0HANEfIfjW2P1GPPa5su3WU/fEYvuPDw8xPX1ddze3sbj42O5LP4///M/G41xOBzG3/7t38bp6WkcHR3FyclJbG9vx+PjYzw8PMR8Po/ZbFYuTydwyXcnMyb6nMGTHfT29nbtxdO2U15j7ODLy0uxN71eL/793/+90RjxHbu7u3FzcxN/+tOf4k9/+lNcXFzE3d1djMfjsqbdbrciq3zPXZ3Yh+xH8j3MBgD5/mkDn9lsFvf39zEajeL29rbcC9rr9eLg4CD+67/+681xtb5Qm4uvcVqPj4+VhfQF0jbEXphut1u59NoOh0up34pEMvqiP4vFInZ2dsrl3PP5PMbjcbkwuU3DwDEWX8bKhct2nhiqfBFxRHwzjiysvI854lm+VJvPMGcsvue86WXa9MnKFRFFIXg+CucLa7lAl/Fkp1nnSLNiej4Yc0aQjJsou9N5vcD68fGxceTAHD0+PhYQY0PofrlPzIkjQkevNsTfQ/42aHVyyzp3Op1ycTEXMbdpyMXz83PMZrOYTqeVCNT9QZ7rnEkeS3b8tO+hf7+j7pm+zLlp63a7xZhltic7TtbM69sk4qxzIpZp/x5gFxFlnP1+v8jY/f39N7r7Xut0OgW8cvn3y8tLcZY4sHxhvd9TB+AyQMDxY0fMZuV54qL4url5enoqc950nLY12GdsrO0XDt62BCfqC7ANALJeZ3YE0IZeb29vx2q1KoAPGTcg4pnv2dZW2moFAfXSCTr7/PxcJh4Dwf+zc3G0ymdtyPgXmsuOli+cW+4bxnM6ncbe3l6bYZbIKCLKQoHi9/b24uDgoDYy8XgsANkA8S8G2sJq42IB8t9aQHjv4+NjY2G2ce31erG3txdbW1vFCGAodnd3y/Pr+vFWy4aHd/Jsf67OECO02amxFk0bkTvGIxsLP9s/e0tW8xg8j2+BgPxzy3jEK3CZTCYxnU7j/v4+Dg4OGo8PhUcXZ7NZPD09vckUGMSainME7TVgLjweN69bNmZ2pKwnIK0NSOh0OkUOScsAVtE/R1TuT44i/UzPSZY//5ujOK+f9dZs03w+b+VAPQYDN4C87SwMVqYc33ouz7KzzWtuFsh2id9FrJlEQLTlqEmz/phFNBXvdcXR4TjtPIlIrbd5rPwsyzHfM2ZkyH3DhzUByq0dKI2FtZKw4KZgvVB0vs4AMaCMpLIBwhAaeRrFsMARUUHmH4nQjHJwoPv7+0XIPS+5/xnp2+mbWvBCes6YK1NH9M1/73G1Rb04z93d3ULZREQBJWYO6I9bnQL653ntbIyz4XoLHPAzUGjbCBSAkt9vY8j3OdfdxFnn5+R58fOs3Eb6vV6v0JNmFpqMESNEOuOtqCTLXh1Tkp+do9i6MduwZv2NiGLwkbfValXo3CbNwA2Dyc9YW8Cs/wbbkMf21pjeGqPXEJBv/TTrBC3fNgJlbHt7eyX/6UAA3bTDtBOgmSlhrtGjOpCUbVjEt2kzZGVrayv29vaKXmWw36TxvExBA+YYu6lZg4q8jmYrrVt1c89c+Tndbjeen58j4hXIPj8/l3QDTI7ntK61pnAjolC4OQR3EpjJrUNzHpRRsRfEToLB+ns7USNgIimMiznvJq3T6RQFt+KzmHW5kuz0PbaMbPMc5L97K0LDSCH0zp8yJ20aAGF/f78o23uRXu63kWpeh++NMY8v/yxHdmYbmhreuj7RAGG5XzbQ2dlb0RmfP58jn6zc/j2GhPXjZ5PJ5N2owg1jtlgsKsiZ8dVFhrm/dTrp77PDzy07UQNaPw/70Nboek55Hrq4XC4rOc+3dIvnOJdLnyK+pZTrolL/3MbYxv3g4ICCk9aA3XUiTkt5Lj0XdSDVTjJHXHmOchrDOuvnW2awDfl3TZojVvyG+8YaeD3rGDnXFdQBAOsrDfuW193+wrUC+/v7Jd/7HqBt7UBdzJOphExfGhnYUdYt4luUH9+72MYtG0me4YgYlNGkIcz0lwjBRSV1ymUhdw7Y1I/nwQueI+hMjXi+MlWBEfme8XhrjFAhtFzdmxGr+/69CK0uArIjdKT3PSW0or5nyN8ao6OV3KdshMws5Pm0k7UDdf89J7m/GcChN8io0X5TsIc+oY9Z2W2EjOZt9N+Kzr7nYHPkw7xgXFlfV6bSzzbRp9+Zm9fLNoDfOYJ677nW1/dAoD+XbRgFU/v7+zGfzxuPz7JEfzKV6FqErIPZZmanyxq4uMvPyJEqf1cHHpAlg7SmDcdJZJ3Hb6YIuXXapQ7AmyWzj3kr1cL7+DnNqUQCJQcob7UPFRF5cTPFQAczZYQTy4YM9GNjmZXCDtpCkhFyVvhMbTVpnU6nFB2xCEaHCKTHGbFGsXVUgvua6RiP5S1DkQXH46Mqrm3L9JNpMguzgYsdH+P7nqHJCphZChQxG0ArNLLRhE7J766jwPP4Hal9jzXJEYflNAMLGzaPifnEKKIX5LiQ9TYNeQLQ8i47wuxI6ygxz3uWwyyD2cGwrgYiGDKem7cTtXWiBqAR66jCfc/Pzo4kOxrLL3NW5zxZVxff1IE/A9M6kPG9sRmM1eU5bR8x8HWRo+c4R4+sf65Y9RjrwLLnlTHWpQG+11arVaG3kVXmvdvtljoW6xlRIXlvAoU6W+l+ZpvqgMS6a1vtn/Ne50Hfaq0dKIjZ4W2OPhkEHfdAtre34+XlpaLMzlXYQfnZfl5+Li1HhM4jNEX1OFCoBj/XaC0DASOyLLT+u4h1kVIen+fA48yOi/d6TG3RoOloI1xHnxnl5mjrewjdkSz9tXPw/DkSyAbJfWxTtEBz9Om+W/7eGo/X1v+HhciK+D0A5GebEbGxjIhKEdB7DWABoEWO7Lj5XJ2uvLV+mSKso0izY4ZSNWh2Hs762GaMrFUdg+C+5r69Ne5sUO28eE+OePxZorgMmA0KMcBt9DHbTX5m8JiZD/pkB4qDdcuRXK7h4F3ZgfP8ra2teH5+/kY329DUy+Wy1MwQnfvZrKEjQIM9AwoXrbrfWU4MQIh4HUHbl3ksPAvG8XutdRERiNmHKNi729i4+pYFdLUpgua/tZF11ZkjEBssvoyu7IQ+ErlkqjSiGmHaoDN+3ud++Iu+sJAZLfr9fDFfNPP+NrxW6KZj3NnZqTiCnFPmc1ZU0+M2TP7edCGFSPyNBZZWxyZkytZUeNOWAQt/y3gcZXteDHbqgAvRrCki/13+8ljz9qQ8ngymmowRXcSBGnTUjQ2EnXNgOcrg53Y4dVEcDcOdx+4q1Qyqm7bt7e1KyiiDactNdvjMK33O9gDZzPn1txyoZd7Rq2UFo9smQjPQ9FybGXEzyH7rWfTJ8g81mW1lBpc5MMB2AYKso00aa8bWR5yW02xE73acdWPBwQIYDA74bLfbrWxRwQnnaD3bH+YCAISNfKt9yIF6P5KNjT9nJApys2PCw7NoFnwGyATbQPgddTQoz25ahpybnaMduoszTCXYQEZErVBmB2MwkfPALLbHy2ds9Okj6M1z12SM3ltn9O118PNsmA0c7Ewxojhn0y701fvoDCLeMobZqLVtyA80UY6y87PpR86fMTesmZGyIwWj42xYDX5Me9La0re8k3RKnqM6GjkDlYh6pseOLkegGKW6HKOf7YK+/M6mjf6zjtmQe86sT3ZwHqfnzuuT5aHOrhl82bYZZDHutkxJBquuvcDGGHBnEJsZB4+B70370hwY5P4wl+gP9p9oNM/Ze+NDf1hHb8GinxzKgW6hszRsCwU/dQcpLBaLyrY8O19Hm7ZzOeIml51tUG4fyoHWdSob8RxdoezmmT2xjjJQ0KzUfo8VwEqV8xQfaX4f79zd3a3w4z5uy0j9rYjOyuZ8hBXA6AjUZ0PFszOiblNlzLvYk5fpD+cfDBT4O/qXnWdENfr0M6x8Ziy8pp5zPoNiuN9to1A/z0aVnzlCzuvP+Jy3ZO2cm2Es3trlv6V5PnME4TVuupbWP/4+U3vIi5kPp1CyM7QuZdDH97QMYHN0aTDL/+l302aja/bLhVeOEAHryJ0ryler1zycK4Xpm8Ekz6LPBnxetzpg4b9tKqv+W9YQO2GWzqA92yf/LS07CiK8XGXv/ns8rDW5S6qLkaWsN+81U+URVYaR8fjEMMAD+9TtOH2ggoOBDIptp9g9ggyZOfIhMdhlGJXfNAJ13tMePb8kUzx5ketoCufhvJgZPVjgXIRhg+6BW8maNC+mDfn29nZZPJyEIxcLlhfHiur+1c2D6S76nfNG2fBSKNV0jDjQ3H/QV3aAmULKhpMG5eFN4UaGdrw2SswHazmfzytUv+exjVFaLtcFb9vb22VdeS9ApQ64OZrEOTJ3bNngZ/6M6wNyRAmqzkVafo8dUJPmaDkDHSgzKDdkmM3ojkp4jvceMhd2LHYa1ukMrGk2ajZmTRtygT5yWISfY8fhZzNeopjlclmKQ2y/+Gx2hrZhdWxERDXFYJCY+/JeM7vBWHZ2diosFOPGHnC8XwaeBpp8j+2KWAO5Xq9XORbPoJl+LJfLso9+Pp9X7FMbMIttyXL//PxcnBoBFn6Ao/siXk97Argiv4zJdspRZQ5w7EB572QyqcjnarUqgMXA5a3W2oFasXLlbZ4wIxQLFZOJ8GUqt0444bwjqtQfziNvVbFRaLPYCCjIDiEjpOdf05RG8R6HKQ+EH/TnCtScs8rGicWuM8wIIc9v0jqdTiU/ybvqEvggPiNWgxkb/reeYcaAtclIEWeH8JuaztFa02ZmIGIdTXieXJIPleM0hZ0KzUruaNryliNWxuHck6MI3tPWwVhWzcjYcKBzyLJPc/HG/azX/lk2yAa5zKvHbmfq8bQdX0QUHa8DypY9gwSM78HBQTG2eZ3M3tSxG3VAip9nfQWUIluc09u00Z+61NbW1lY8PT2VubBNeHh4KPPD7wyMDZoWi0X5Hv33PGHfkImXl9fT3ACMnHsM0G0LEHju09NTTCaTGI/HMRqN4ubmpuyBtn/Y29uLwWBQyZmSAmLOPf/Ic04/IS9EnazT8/Nz7O/vcyB+xU7VMQp17f8zhZvD//w7EIeRC//PxqWuOTq18bOhQwm8oDjUnGd6rzHR/D2HDXBCBdQBgpbpZCPhTPnk9xjpgZDsZHAsGGuUMlOoj4+Pldzie80OlDnCiJjS9FplwXRuCyOeI0aDGMZkGbDh4+em3jx/beki3u19wMwfjj1HyzhuyxgRMZFFzo+6aKyOKst0EzpCBEHjXW2jM8+p1yxHw3ncIHkbHeuw19d5IzNDBkiOjFxVmUGMHXzTMRJ9Ukhkncv1AZ5zjt0E8Nqx0I865orx45g6nc43m/9tu2isOzm4j7a3AEp2DKwtB717e4j7xAlC9M3yy7usD6Sr0L+np6dypB6HRSCrTdcRecG+2nne3NzEw8NDhfnA7o7H43h4eIjpdBrckgWwx7cwJgNbyzOfYe0YF4CCsfM7M2L0/a3WepUd8TkCydSYQ+lMAbFo5JF8ruH3PL8NtgsKjEhsoHPSuGlzBGEjixH0AQQ2qu6zowvnKnLFGH3O9JkjUAtqpoUXi0VMp9NKJPleY1zO7yC4GD+cGXPtmxEQUhyHKUTGgozUGXkLs40Q/ccQYoRz9NekrVarbw5XZ9wHBwdxcHBQ2ARHKNzCMx6PYzqdRsS6sAHKh1NKeN5gMIjBYBD9fr98z/mdw+EwDg4OKpQYFx1gTKDn7bSarqN1xJEV8uSokHmx8/NNFzh6V2HyDhs3dM3V5rwfx41Bc3MxTNNmQLtarb45yKTOzlhPc8Tt1AXOGWeZ86xZ7lyEZj227PPejzpQxpCpTttd64k/a71j/jmknmfTX545n8+LM3l8fCwRqZkJZKaODWxjc7rdbolquWEG5+9jYXOKYzabVdJ7zO3Ly0uRV5xu3p5HHz0G6wz2gD7mwOA99rI1hTubzYoRMTo3bcQk5JDaE5DRf13OLIfSGBnTXo6OEA7Tuc5VtWmm9XJk5txXNlLum41ORFQMliNTopHZbFYWzfkwG6vsiBx1NDW8zFmmK4iM6IPBjotn9vf3i7Pwnjf6NJ1Oy1VMzlcZ9RIFASroP3PivKuNftO2Wq1iOp1WToQBjdN3/uV8Ywzq4+NjDIfDeHh4iNvb2zKm2WxWrtJ6fn6OXq8Xw+GwGMzDw8M4Pz+Pk5OTGA6H0e/3o9/vx/b2duUqKht+553s6Jq2nCO28zSrANBx/sxo/uDgIIbDYUREOd7RfQKR54JBR2KZNjZwySCqzToaJAPk7AydEnGUaDuSAZTzok9PT/Hw8BD39/dljbBxyC86U1cX4DWjj232gTJGX96AXZhMJjEajeLu7i4mk8k3YALjn+2NATj9IkVBMRA0MIAD5w+75gMbmFPb4zbriCzNZrMYj8elzgFZYuzIIqCTuWZO0UXkGQAcERUbmRkC+x0HPKzr/v5+6d/j42Ps7u4WW/C91sqBLpfLmEwmcX9/XxC6b4Gg5T2ARkAIu6sYMw3GJNi48zdGwUw+C4QgmoKEu2+z2FZY50oMFnIlH5EF1w7V7c/b39+Pw8PDcpuL/wZjb2W0QQBFR0QlJ4qzaRO5IDRGs45qTWGZbmMdDg4O4vj4uJKrwAHxd/f393F1dRUPDw+F0sLogYq95cUG2qDDyut/32uLxaK8G0OAkxgMBmUNspGjj0SQFG/c39/HarUq0eN8Pi8yHPHqdE5PT+OHH36I4+Pj8vyI17tM/3KBdJEl32VpRTf70KTlyNWgzsArIr5JB0D5oUc7OzvR7/croBRAaPBoJ2r9zWkcU7nW0zYNB4de4DRYQ1PjuSAFepNoC1mAfSAXhu6xvnamGGMDBlexOvo0HcoWiKZraJC/Wq0KAL29vY2rq6u4ubmJ6XRa5pQ1BQRB0+7s7BSnz3pDYUdEySVbd12Is7u7W+46JhK1HUd+YCWa2pzlchkPDw8xHo9LvnNrayv6/X5sbW0VOwaoPTw8LFQywId1gLHEtmY7RTopp1MYD34C21sXnTI/v2kEirARLflCaxbL0aU7REcYkFEgHc5OgM9DRSwWizg4OPjmKhxHa47gmFgmqekYiQR5Hl+m4Vhw+v/8/FyupJpOp0UJoft2d3fj9PT0ddK31odGY0xR+kxvuirO9CiLz/Pqqj7fajwPmtrGFwPBewwg6BcGlWgUwYyI0q/Ly8v4/Plz3NzcxGq1in6/H8fHx3F2dlYBUBnlRnxLvTsn1LSBVDE2yBx3bvL7yWRSAXO+ABolhEa6v78vc4OM9Pv9Ss4Go75cLmM0GhU5mEwmJRq2Mdje3i4/dxTXtBFRgqox+pnejaimVzBOOWLt9XrFqHa73QLqbDiRw5xewODQDxy5o2w70zbrSD+gmg8PD+Pw8DD29/fLvAFsibJc2UlEsbOzE8fHx4WJMOCAXeNdrgolKst1G3ZmHl/bm4OwMY7esSdcOO0insxidLvdUqthYG/gSBUu480Urdkm9ABgjG0wXWyKu8kYJ5NJTCaTiIgCUnkWawu4IdDATzjXztzDpOQLx323MfKCHBJlIzdcecnF5QSFBt6/qQPNJxBBJYDsQPUOnU31MEmDwaASUTmq4u/skK3wviEdJTY1RqQasT4arSlSYqGfn18PvvZdfEZCzEdElCicBZzP53F3dxdfvnyJq6urmM/ncXx8HMvlMg4PD6PTWVeC+XxI33CDECEMtNlsVgyey8rbGN5sxGxsocVYX1cqojQApp2dnRgOh3F8fBz9fj86nU6Jpr9+/Rr//d//HZeXlxERcXJyUoCEo28i60zPOgrNBQFNGs93UQEKiPODNaHwBCcbEUWRASfT6TRubm4KJRuxzk8xb86BOnLyOJBXGwTAlMFgm3H6b/N6soZOLdT9DiPe7XaLfgJg+d3Ozk6FEjcz4foDxpyrxu2A2owPfSTCsk3AhjhtArCHDWK+AeDL5evdpFR4OjfnO2ShYU3bAvqQAfroeSeYaONAcfie04j1NWfD4bAyx8gufXdxmBkpO1BAhMEIThfbzbyyTo7CPD7Wt43N4cCEg4ODyuEJyLwDEmwtjtwABvtBKmUymRQHOJvNYjAYVLagbG1tFRr88PCw+B5Xd49GowJWZrNZ8VM5Z5rbh04iMmpxdRb7ljL96gIa89wsKAgfxM6+PXJIKDOo2AgY9JKr6Xi3o9ImDfRKxMU9cQg3+4YQzohqxSP9mc1mcX19HZ8/f47ZbBYPDw+xv78fP/300+vEb60PUXh+fo77+/siEFb0wWBQUQguXyZXk4sOmjbndB1B2Mnc3d1VoiecTqfTiePj49je3o6zs7NKsQL5vqurq/j555/jy5cv0e12S5l4t9uN8XhclCFfmOvKZvrpSLypUTKFaDoPg4rRQaa8ZccolWeNx+M4Pj6Ow8PD6Pf7MZ1OiyHe29uLo6OjOD8/j/Pz8zI3FB2xZij6y8tLodDH43GlGKuNUYpY54dznpjnOD/OOLe3tysVqN4iASCGyoUaxdHwLJ5N1OK5NpXP54i27bybtJeXl7i7u6t1SLyHSAodxC5gXKFnZ7NZbG9vx6dPnwogJi8ICIYmzXk5U+zMM040g1dHSU3aYvF6ld3BwUF5/s7OTgwGg4iIGAwGZduHt5GYeXB+F7AAM0Lawk6M4qGcT6Y/gEx+BsMGo5bZh6aNPjq15e07jJ3iu/39/Tg+Po6jo6MYDoclrfLw8BC9Xq/khUejUWxtbZU8fr/fr+g+EagdMiDh8fGxpJxGo1E8PT2V9xO4vdU+7EBRTBAPi2IKhwkmHAa9g9BQvNlsFjc3N/HLL7/E1dVVCcNPT0/j/Pw8IqpFARnd4tAzrWCH0IbCZRzQdYT1oFpCfFcuOrcHvTAej0vyf7VaxdXVVdze3sZkMonBYFAiZ+/pIsIkogUFMa+uKkUgyUc1VVhTNRHVgxHIv9zd3cXV1VVcX1+XfrH2GI7z8/MKY+DKOSpZR6NRUVRoJG+7Mf1J1SpOChnBqbahcU3p47QoPmDeoABRVP71eZxEPcPhsOQ4Hx4eiqycnJzE6elpHB4exvHxcXz69CnOzs4KbUS6w7UDFPBgrCeTSRlrG5razsmOkfwnRhXqjrns9Xoxm80qwIzxYlBdiYlzIfoiCgWkWFccDWPYcfDIXhtZJdIAoDNuIkaAbI60iUSRwZeXl3h4eCgO9Pz8vDiau7u7uL29LQVi1m0zajiT5XJZeTf6SWtLbwJYqfZGDtEZ8vmPj48FTE6n0xiNRpWq8F6vV9aNPlDchkO5ubmpHEhhEA0QQVZcNEQf7+/vW29hiVjbHCJ/mMLhcBir1apEyQAlADWpn9PT0zg5OYn9/f1YLBZxeXlZZBgdZ50oEKR+4fHxsegdtghdY33RTQI4dIW+vtU+ROHa4CKsVhxoPOcJcS4gP37O4K+vr+PXX3+Ni4uLeHx8jL29vYIEXa2Lsjh3ZyNOPxH4NlELf8sE4uAQOKIJBJbIYzgcxtHR0TfsuxAuAAAgAElEQVQb01FyDPd4PC5fh4eHlfzuwcFBTCaTgizz6R8R620CzHVbOszNkQCOkXc418L8OjpyjgSHA5LPORXTerwDA01Onfc7b9bpdIoS0N+PFKB4yxOyBOjDwDI2AzEaira3txdnZ2clr93r9WI+n1foIuSQcbH+LtNHge1cPG9tmkEU72XuHd3jCIg0FotFjMfjbwwmhgcwQz+N2nd3d4uMZqYAuts0KL9zCqeueOt7a+jcresAnBtfrVbx8PBQgApft7e3cXNzU6K2wWAQFxcXJaXw8vISX758ievr65JrhAGDxicqx6hGrE8Ai1jXNCADvKtN2sjpn4gouoXu0A9swWQyKbrpiLnf75c0BDLPOHCYgEl0HUdlOarTN4Id24Y2zUVDw+Gw6DrRtg9soS6Biv+jo6M4PDyMXq9XahsIPAAe9NGMBzbTNSTYdf4WWhtbD3A2df7mmNpMAJ02TWIBx8GCbly9BRJGOcld4HDhn0ejUWXv4cHBQaFxnSDPfDwLBEpkAhCcNs0FAhg+03+gwHx6B8rsgoCI6qZtJ7xdrQciOzg4KEqcKzQZr1GjDVjb6MVG2/kV5hJF3N3drVRaHxwcxNnZWZydncXJyUlxdHZ+PnKLqJUI8+TkpFBKGBuiprpIjD61yWX77zEkPMM5WOgbjA/FKeTNkF0Unmh8uVzG3d1dAYUPDw9xc3MTg8GgGEEcI4pKUYuL28ixN9lzVtfMyqD4pFacO2L7FP0FlHovNkUbBkXkhdFJdMBGFBAIiLLh8u99IEkbJgHQAbODAWX/s40i6RIcKICVOR8Oh3F1dRUnJyfFCV5fXxd61FufptNpKVpcLpfFOQEAzMj4ZxT5NQVEMBUEHvl+WBy9Cxonk0lht+gDdRNETYAj75VEt5BLA9tcTc/8m2kw0GyT58VfYCex06ytC9qw6QRgLjYi3TUajUrKj7lGX/lCz5Gh7e3tYsMYH3ro5xCtw1J9L0j58HEZuSIKh4NT8OHrII6Tk5M4OjoqtCQogAHwhZBgxI+OjmI+n8fBwUF5F2jWtJFL6WltboZ3y45pOByW92BYHIGBrL0h25EYgoYw8vu8yXs4HMZ4PC4Ilr9zcQSGOKJ6CHYb4+u/B5igqMy7DShOP+I1vwClQgQGhYYhB9VSMIAQ8mwi8Ii1YrCuLr0HOWJQ2hQtoECWEebeYATj6+jahS+5KhWHD2jodF6Lp66vr0vhGQDRdCM0OP93Phuj9BEqHoPowo+6vLFZI4AI6488e1sItDCREIANdO/iOvKENrjoHu8gp/SRPZKmRKGVeYbXl3oKUgjMMZ/3EXIRr3oAq4CTcFGjD2wB/JIbZewR6yjbf98U7C2Xr1s8oI3RPfLi3u3gXK13P2QAiEMyTQmb4JxuroFwSi47b5wteuPnvNdgPewTcsqHE4eWy3WBYq/3urUF1uHp6alQ7tRnoIMGMvQTQOBgA/kHNJrFxCbTR2pQ3mqtHKhzZ65sRKlyRahLwMkRDYfD4mjIEYIkoEcdoYEgoU3zkVy8x3SxqVxyUW2Mkr+3QQEt8bMsCC5kYAEzBQ3wgA515IpQ9vv9yvFxPA86FyQeEQXRty2bB3DQL9O4gBBTOuS5yDEcHx/HYDAoebeIKI4A1EgRWDYuEWuj6rmLWOetmVdo/jZ57IhXg7a/v1/J7RDlPj09VWTFhUr832vL+q1Wqzg/P69EzNPptBgSNuS7ctHzTSEGYAgjaOq6bcPQRUTF8eXCMqIK1oA1Y41xnvwtz0a/TKfxM7MSZn+sb8gRICTr73vNkSVOC9n13PK9HWg+4o7x4wwpQCG/yJoSQbNm5KxxZD6RyFE972c9m7bV6rU4EZ0ArLnam3d7C6EjT3KIRKCsA2vHfI/H48q2M4MPpzhwwIyFYhtANLaxjQNlG1jeeoTzxP5jY+gTtgOdubu7K9G3mTp0F2frd7OePIsGxc2/dt4wn79pBGqDg4MwmnWDOur3+6VDIHO2etze3hZazIbl+fk59vb2St6Rarp8+ogFwblVJucjuTNQC9EIgkJE5qP8TDfUITWUwpuSUXocsvdaudgCxeRfGn8HQMD4NW28C+eAspsSZ02dT8NgeOsKa2mDyrPZDsEcICveCmXB93xYMc1wNHWi3W63bBlyrgMHYpmgD7zDNJVz6cvlshQTUUhB8QLRFTQeRpdn0G+U28eY5bqCNs10WwYBNOegTQWa0vNxmpaBDAapSs9FfNY/1g/DjfzUbQFpOkYzJr48ArlBtlyMZwqZ6A4HHhGVKJPnuTLbQMBpGN7nCNiFS67ibzo+ywQOxaA4G31v8cvFd2yRcwADk+M8dwbppM0M5Fx0k6nRNg6UNAfPB8SiD55/76mG3YIhotCHaBUbkg/mYX0YF18uMuO92Kq9vb1S7/DDDz/E2dlZYT3fah+icE2j4lhYZP8c+o9IhA46V0HhDEpKFEfe0VWMk8mk8PQIh3N2Nq7mvtvSYo4gQGX573MOlndFRMWgELGajuS5jnKsEDZKuaAFR+b8CxFx04YD9bz4e9OerCPzwGlKR0dHRZFAe6aWnfMGrVrhcnGIqe5MO34kMut0OiXPyjrZgUCR27CbJkLZIqLi0DFWGGj6yHOQQxy2Db1z4D6Vxc69bSGR142xslZZHyKqEUfd3zllwNp6m1bEupoX9gF5Mp2L8ed5OOePFL4BbCKqtywxfgwx64djR/+wGRzbaF10qoYvFyvSd8ZshgJgBNgCHDqF07R5awr20awac5BZQBgrxuaiO9sV16EQrRKsABbyQR8eO82psnxL0/faYvFa7ex9prBfOc9NFAwYhSlYLpeVQk5+xt/mfaPOm9thMsesG+/z/Pzwww9xdHRUwNZb7eNXBsR6kZhYFIYOOQ/GpBlt+dSUiCofD0qBunD+D2Ps7Q2mZ/wcL0bTMTkC5WcIMEqa+XUvlikFO2MWDGNl6tafxdgjIBh+/pbFpjgmR2xNGvSO2QM7bztZ+oYD7ff73xghG2EbHPb68vf0Pe89y1Ema/gRp8LzfKZrRJSIEYe/WCyKk49YOyPLkA3WarUq/Tcq52/58voR4TgvSP6TU6uIlBwRNmnIaAYlNOTCsgdzlCN69BaZNpNi4JErsXFUdlimAemn17Dteno+TMX7/3asgD4iVzuaXPQHEDADYTCRGRL/zmwF8+8iy6bNzhf5IG9rgE0DLAOUnFd2GsYFeXW1G1CWzB/093w+rxSZMWZ0m9+1jUDZzwu48i05PAewy9YTIkjG7CiyLsiwLSXwwSabKXAel/ngeEiCBKLf77UPXWdm1GaFd87PRQkMxrlJnA6Tl5XNqDbTWwiHjbVpKRs+KMo2DtSOxe+0M1ssFsWJeK8dQu8x1TkGz4MNNGPOEWGOqHku42w6PhqGxo7ZiultFxgQU9DMC2OnXwAbHI0VzFQazITBj/uW58hRSJNGDjRT7QZlpjYdbZgStbG0AvrLslm3lhgljCPI39tbvAZt1pL1oR9Q/v5yyiUiKrQdsmbq1VGl5yc7DNODORLI82An8xFQhHPASaFfBgAYROswuuFcrOm+nOc07cvf2hFhBxiz7YSjUUffTRpzS27WKQ2D8ZyjZuw8w/lwO16zPWZLzFQY6Jgh4j22AW3rLpbLZdmH620l5BxtK2AfCZgAugQY9gf833St1xA6G/BqCp5xACagt3OK7nut9TYW5/mcf3De0cUppokslPDaIFXnXFBg7+GzkeWZPJ8JzEjXdEubtrW1VTnY3Qrp3EIu/18sFpVN9m8Zovx/RzQY+WyQM+1Gv+pyhk1aFkTnwhif6T6vj+ljUFun0ymn7eAgc1k8KNi5cRSqLq9mx+nccZPW7XbL9gvy6U9PT+VfgyGqhInA6aOND8wJhT/eykXFOBQmim7n6+jC+oPhwAG1daC8w87TDsYOFOcYEWXcRBusEbkpwK7XxE6UZv2lPzaEljd+hl40bQbs9JP5jVizTMgwFbfQoLYdmSHBgDuCc/Uwp6sBxswyZECcadY242NOAFo+orAusmf89C+Pz591dI4u2V442GAesAWu5M6RaNsxTqfTArbRCd7r1IHXF6rY5wiYyXGRE2uHo+71emXbJL9zvUEO9mAmXBjK/LzVPrQP1F4/5xHsILPTMM/N5zFAOMq6CNTJ7hyJ1tEpPPcjDUEBmRMh2glDB5HXZY/qZDIpSonhJtpx9G0qjHlA2J3Q995AnovCmjrO2xWarKOje/eD55lO9jYC/nZ7e7vkUtjmQJU0DpS8jA20qRMf/8h2JmTGhU1G/m0cKOjTBtM5IeTINLTPB3WxScTa6fg0KhRzuVyWnL+BmwEO4/D8MlbnW9s0R0B879QCc8h4Mb7OuRm4cYONja+jbTtSjDDjdfRi4OwIFCffppl5sS2x4cf48U7WxPJi9sYsih0UOuhDBxzZYt9s1xxx2oG20Ueqe81oMHcR6zNvDZgYb7bBAAKPxcU0trOWGVcA8zOnJpgr3tMGBCEDGWxg73g+jjEiKlX02GCcIGAd3+AInrt2sTfIxt7eXuUaNUf41lEa4/7NHGhElWI1ZYAAuXM5oQ3CiYgyaOdmcExMtguGskHwO98b7HuTkJspkUyFbW+vz+hlzxUHDnivok+6eH5+rhzk7PNRMdY8n7ySczBvUYZ2Dm2NEuNDkG2IDXLcFyNYV8mh3M5HME/Hx8eluhBlsdIyd0bKrmC0A23T7KiMnl2s5TXGgDhfv1wuKxQrdxmyiZsiICjaiHUlOqCBNQUFY/yQVxC1WYc262cDy8+yrtgA4jx9OpOBAocUYHisV5nOxcjbeNf1LwM/+tV2nNkpoR8uAGF8jBXn53RSxHoftIG52R6nNgBiEVWAg6xnZsSOuun46HNeN9sdM03+WZ4TOyczH6QT8r5J09tsTTNAYszZ6ebUy/ca6+J5RuexkWxpce7X+rFarSrFdzhRGCDsrgtUZ7NZuZQD/+M9xK5Kp1bDrNd7QOhDDpR/F4tvLz5mUngpxQY4ClDFYrEoydqzs7OCTA8ODspFzLu7u3F0dBTHx8ffHFiQoy5Ho/yff9tGZ/TbuSEQKFWYlI2fnp7G3t5eOW+VhfCi4BQ4oP36+rqyrcPzwTugNXq9XqWyz/QjBrktfWtwkw2uf2+EDcJDAQBCnAbz8vJSDkvnVI9Op1MqBCOijMlGwsgfQ+JctiO3NhQuhhN6h7WEromoHgaCAdna2iqOxEZquXw9k/Xi4iIuLy/j5uam7E+2Y+RftvjAEvB/jEI21jZ0bVuOeDLINe3I76HGqE7lhgpXuEOD4TTrCuJyP3IzE+UIrWnLQN15aa8nYA4nQX8odKGAyA4UufU+3MxKONXBvDAnBAHuo8FKmwhtsViUvvEMgz10xGvsAhxykma6cFqeO8AEh66Tetja2ioBAbqdo0XLKs65qQMFgLIv3xS1K76puEUWGROfub29jS9fvsTl5WVcXFzE/f190SfmDH/DndWz2SxOTk7KM82IzOfzStFRDtZ+0xxoplEiopwdyCQZYUSsHSiUno0XgsnewqOjo7i5uamcLrG/v1/Om3UVXT4FI/P0/vcj0UsuWQfBsKd1MBjE0dFRHB0dRafTKRVjjtIsABGvBUYc+UaO0cLN51EcGrdIQLfZKXuBm44ThWOOHU3k5qgQYYt4Re7c1sJnJpNJXF9fx83NTYxGoxJ1suZetzr2gS8qjOmrEW8bo8SeRZ7raIg5BwR6r9zj42ORQ1DrYvF6ksrt7W1xnCg7QOD5+bmcMfv09FSqgJ1Li3g1GnbMi8Wi7INucwRclnk7Oxu/rAPQ7+jl0dFR0U3AordGcVgCgAKj7Epd0+B8Nuf8HT21aaY0DYa8VQrnaLoPR0C6gPyb5cnV/b5OEf0z0OTnzpE5F4r82D42aQaqOGo7EBcxuS/8DPn13ZnIFvOAHHJBxWAwiPF4XLZkwSodHR2VIMcUOI6OOQLwNZXV5fJ1CwrpHp7p4AKm6unpqXJZOro3nU7j6uoqfvnll/j111/j6uqq+AqvDakl/5w5MJsCcDBQyUzOe2mj1g4UwxuxpjDypmYmzNQOyVroEJcP9/v9Mpm9Xi8ODw8Lutna2qo4TQ/YA61Dw1a2tuM0/4/jBNn4a2trq9BhzE+/34+Tk5OYz+exv79fcqDOMSCEUBYeKw7EiB3nyffOYzTh6vP4MISsD/+62tCNCALD72POiIwnk0mMRqPiQHEwoFvGb6rF9LVRN04Lg8d8tXGgBm/Ik9MLPr4Pxw1Sxsm5kpefYWS4ZioX1DE2V56j2DgWO1CAEA7rI40xOT/or2yc+RsO6uaITUc1sA6WM9YK3XfExjPNrBA5+Pdt8oMR6zQCf4eM+BAR5yixLYeHh0UOfBIS/XMu2JFafp7pUzM+OCXXW2CY2xRKZYfLGHwzkHOfBumec8aJzBJhr1brE8+en59jOBzGzc1Nscfj8bjYZN6LbLLGzJNtPpXLTRoOdDAYVIrQADG+zNzRrm/+ubu7i4uLi7i4uIjRaFS5YpF5gHEwy7ZYLErtAp8j4mWLi1lG25z3DsT4kAOlmML7aQijs/HNFAcD5gD50WhUTiNy6TL5GUcNpkihA/37OkV1YUHTZmOOkuTDsEE0FJHAww+Hw/jpp59itVrF8fFx2XcIBcbe2MFgUM4H5gQRU2lQUXZumZ5G0DJ6arKOKBSO2k6szsABgIi+I6JQtr6ui9wESBVk63mD7nXlJCXxrJkpv4h1AU8bB4rh8KkrpmsxmqZwcO5U7mJwGbvnZz6fF9l1RWDEujrV0RAylSncbrdbQFYbIGSnyLsACGZgrD8Rrwaa6Nh0nR1kRNVw2uihe3auPMPf24kaTLeJQJmLXPhBxOW9hHzeMmcqmu8xstZJ5gWAZ/BhJ+pI2/NMg1VrW2mc88QAcQNMIidsoGWFiBA9MhWPvtMMkOwkkUHXZaCD6B7gifqONpF23heNfceJwoi5ip819E1VfCbi9Vxu/BLyQP9dVYsMGxgAdpANM1KZWXmrtc6BQkU5hM85gIhv93O6copc4NXVVVxeXpY7Mvk9kYH3GFKl6dscUBoE1lW6RmURzR0oz8UxIUT0xXnYTqdTAAEGf29vLz59+hSDwSD++Mc/VsqtWSyfHnJ8fBxnZ2elGAkHyvhZ6LeKMYhcmKcmLdN7EdWcrw0ov9ve3i4On+0hvqmGmy+gVFarVWXTNvld3s/Zn7wPCsxOh7Hzb1tUj6GDhsVh48RzHtm5FlNj5Ly5UomzPLnHlot47+7uymHYuQDE7InHwbv5arM53eM0fRhRLapj7gAMOA4cAiifYjevCYCW9UHunR5x1Gm5MV2OHJn+bNJYBxt71tD7GTHsrF/OjdJH6zR5R0AWIKEuAMi50dxHfhfRrriGv6dfAI5ud33NoSNQojL+z9hggHCMOBqvEzLAgfrj8bgcpM9akZ+0vDJmHKYdYZt0Q8T6xCXW0UES9pP0GJePAJ57vV6pJQDMOj0IS2jHTKSMDOf89HK5LFu5WDuDqPfYkg8dJg+VGbHmxiPernYFsVAMQyXj1dVVKcYA0XAyC8IR8YqYiHJ8m4ALceq4aoxnW3oz51Kcc3EOBNBgahD06zMUETpXoXm7B5RJphKcHLci8Dnmn2c1NbwGO86j2JB7PnH45+fncXx8XNaDC3azfESs0Tz7RL2VhUIhbpV3FIoc8YXBb2uUMHrI0O7ubnEG9NPUG3/D+8kTosxc6nt6elrWFooeKoyclaku0342hD59yEUqbINp2gwWvfmbefWcW1eJfvmCRqtjOvgevfC/mXZm3q2TyJkPMGiqj5bH/MyczjEzlvf3mf51Ht86ZWDBPOZiQBwcv89jB5S1kVVshrfRAKB9yEC32y11CIAm5hLG6uXlpdx6Ynn22jiCJO/I59hH6ciXsTpn7KMum46Rug9kn7m2/PruT7bIuaDPxWCDwaBcUgKwRa+5jWc0GpUAxzsAItby/fj4WGTMQNAR+FutdQSKEOJA4ZBBTaZo7EAoKHElKgUZ+UDnjJ5BLST6yS85wjSt4gKctyjJtxqoxmjUSoZhilgfI+YIMWKdG8nONs+JqRZaHQ3mCNvIyA6uTeSCotvhZfrWBosoDCFl3U3Zk+PDoLoaznvSEFDnTakyNFWVlT5H3u81FJ518EkkPMsAycgfcObCNeejbIxBwBQtdLvdylVTdkjuuxEyiu1ih6aNMVouPQ4bAOaRtbDcdrvdSp44R++uUPSaA3pMixkYMM8AbwpD2gBa7IDHwO+QE6eHyDEz5wa3ppTzXms7eOYRcOHxZOBlnX4LzH+v4QyYU4y9x5/lCPDin5Hn835PMxw8zxQ8P/Oc4oydFvJJWj5vuGnLdhm5QPd3dl6PzTMNC1sDfWwqnoKnk5OTwuD5rPXxeFxJsbH/03aBscGYGXAbwH937RrPwF8aL3VVoScp0wYRa+EmnPY+SB+S4KgzG/ScQ+V8RAtGNrxW3rYOFKGycuScgfMIVhgbGFd/2Tl5zG7On7jKkYV3ZGPaD8TYtGU6I0e5HrMjXhtj5hfKmX8dHdjA5cphjJkRfjYUnts2hsmRginUbrdb2fNlh0VfofR8+LgpTfrg5xBtm44yoPIcYLi9t9f5uDZUvKu40R1TTzwrswo29PSV57kS1YbPwMr6xrPd75xGyZRr0+bnW9/oj6MqH+LusTjFYtlw4VB+X456vb3K47ZjznPaxuZwLi1gwXsj6TP9Zk0yEwYgpZbEFCuO08WcRL6AJ9Y8Yh3N825uiXEO8yPNNgcAxulgdpIR633JFBdBuQMezEAYfFs2SW+ZlnXRUcSaIXRNAnYhR625tT6JKCuNjXvEmtd2RGHjjyAi0HDsOWq1E3KUYNTuajRHoo6wMnprushe6Jy4Z28hE8uEeyM3jsXz4NwLY8TZ1NEl2ciiwIyHv6FyrmkESp9tUPL80E87CypqMVxEaiA3K7fRft4by/usCDZcjpxy/qlpI2fjKJT3ZKNKhIWj5ZxeihFAolBkeWw2dKxnnbyB3m2MbXCJgNo4UFOyddGrDYpbBiOmruwY7BxcYOFo1HJrlsCAhLW2gWzSmBfqLWxvcsRnZ2gdsr4xb14DN9Px6LIvQye6JXpyftZ5+jagvdfrxWAwqJxuRYqEyMzjYW5tp5gD99fODgdKESOAFx3GDrOeVK7iQAh8PA9t9DEiKvQ5847dNAOJbvI9UXWns07zmI18eHiI5XJ9XzF5XhcyevtkxJpdsIzblqL3dTJSGVOrGYg1ZeQog59FVAsFrDAIE7Tecrks+SIbIKPKrNAsKvv7jPCNUj1gnHlT54JhN78P/QciY+z0CyRF9Gjni6JmdG56C4H1iRsgQNMmGTAwxx9xoI6G6Stz78iBvk6n0/J/V6v5PFsbc6gg5ozn8A4MPvlickC93vqqtmyQ20SgpA1w2Bhx05y+3cf3JA6Hw6JwIGBHai7K8bj5GcYJQwxdyKZuKy9yQd/a5AcjoiITjDEXXOFAWTeATsS3ezKdCzdlZkbI8+hiL1PAPNd/g6y2caC93uvhKpPJpDL3OBoYAMbn8fteTht8g2IMNb9ztGzWwdfXrVarksqI+PZ4Tgx903H2er04OjoqzBx9n06nhdVB956fnyv1BOgUtpGCPnY1uHgRBwqDR1oCufE8MBYAZz46rw19G1HdYsKcRaxTPejbcrks78BBUgDkYi+nLl5eXirbfVhvV/t665ZZRH4GUANgwAS9BxRaR6CmMNiv6AQtCmMlxLgvl8tSfeq77/KC4Ij4PcJu9PAWCnLOJyJaG6VOp1NKo+3MXGad8wo29C8vL5UtOXYGGAAbFbZHkMz3bfF1SNKUGBRkrnJtuo4oJf+3QTfChVJirDgFK4GpLLMIyADr5twJgu1N0zYMji74eVMHCop3LsgU4mq13u/J3maXtOPsOCwCY+Q18dq6GGt/fz8+ffpULuRl7JzQhPLn4hYbsqYt59xypW9OLZhuBeA6r8u6+DAFs0rILM+hqAVAYobBLAmyCs3ctPV6vTg+Pq4AGeyN6TXobwOj6XRaPuPP83/LWQYIdaDbbJblPEfFOP2mgHZrayvOzs6K/BNFsusAB0p/7djoB1uqrq6u4u7urjg7zw//UjTDmBhzRPVge8YLlepLFNo2okADY/rjbWWOoDm2D52BHRoOhxUWZDqdVqhd1yqQS/U2pAycbFN9nCfA9zelcDNVa1TovUnmn33ZqxWNxUAoQAc4LJK/lF3jRHO+wRNRl59pS21yzRZHCkas87i9Xq+UVEPfAAZms1nc3t7G7e1tEeK8AAisy+zp/3w+r1CkKKirOh15sqWHBW/qQEHV0K42IH6GIxZHNPycfuec6f/b3pn1tnE0Xbi4WpZIcdeKJAgQIPn/v8Y3iS1r475LFMXtu9D7FM+0aXtGyEXwYQoQZEsiOd1dXXXqVHW1gglFz5oL1DVRw6Q5bv1cEGUSB6oFalqRCU0K1bPbvfXYnE6nNplM7Pj42NbrtXdWGgwGNh6PbTqd+llXXRPN59D/9/z83JrNppVKpchewZlzPMFsj8L1eFQSUZo8dIbqMAAsgAkqpJkX5oa8L0bnEGjcbN46T41GIwdY7ANlpMy+bXCOk40j+Xzems1mxBmSs3p9fXWKkyI2dI984GQy8bPKOAD94v10X2lKhTk7PT21Uqnk86KidhFHUalUEkWgjUbD60qm06kDQFpiYjuVVWAtNEVEJSvsEH+nR8o4jgeAQld03ynLpWk37KvagLjreHx87M5Q88nKTrBf9QpAuhCZmR0fH9vp6alTyrommoLR9rFK7eKXcKQK9NB97QesdPLBccWeAYue7VTEEtIhTBgoViMkRTbkGXBEZhYxunwp6sX56DklnKrZPhzX82pJ8hFmFmmSwOQymYpiQPpQJvRyJFrDQYKKlM7mfZUy0oIA6CIMvVLnSo9rpI6dr9EAABuaSURBVJDUgZrt0bMaRzWYmrMIqSr9vVLR6AjGDb3QfKfmwzW/DPqkWIdIAWQaF/1uNhtv+F6pVCKARQEHQG02mzkC1UIKrdw9BNr0eXQOaHHIUR2MrjoT5kUPgTP/cQW9VIeujAtrhvFQxH98fGzVatWbY8AO6dlDRCMvqjTD1ATPzpofSuswr3EFB0r7RKr5WTdy8Myx5gpzubduU9Pp1M+a6+0d4RoyP7rPjo6OvN+1joUvre8gVcDRp7gOlDESQev4aKwOaNCAAxvAkSsqxzXdo7lnAF4YzDw/Pzvgp4+wsgUKdpiX9+Q/6/W6DYdD11fN52o9B6xQGAxp8wYqbQEDgD/GSYc7wARBGf6DZzLbF1gBPgAeml/97riSTIIm4c32N05ohxkMMQpmFj0HCspXfp6JMosiZo3eGCRKcHJy4gusG5PNpOgsadk8ChcW+6DY5PwKhUIEtRFZ0WWIDXhycuKOVCPokMZAMalWpvJNu4AoMtQNn0Qwusz3ZrOJACIFHWGeTvPbmnc4RBcyFjYMf8c8Kk3P/6FOMQA4gKSN1jebjfV6PatWq978gU21WCx8TUC3mk4gf0mUdnFx4c40fG6cK05J6Wwi7/C5lBrHaKDTgJm4oiBAq441L00xiK6tnrvW6FPBabhn0DnWlXyb5txC5/Q9EBvXABcKBWu1Wv4ZzL1G3brvWQelabPZrJ8nhMUg8jGLHu/h/4B4Lryg0YnOVT6fj9go9jsgJO465nI5u7i4iFzqzflFugvxc00nEZTwvDhv6jGUdtdABPAGKEUPCAJYH/a7rqFG5klrLur1uq3Xa5tMJhH7zucAuInisT2cTVX2x2xvj5QJJdI027Mk/K1W4isYJ5ghuj06Ooqwif9qEREGbbPZd6zAILN52CxaPLHbvXWfGQ6HfgYUFBs+YLh5cRRqsJXX5m8VGREpvufgNhSfRhwooVKph3ICGP1wcXEAmqNVBUchmT+cLYZARaNzQEzS3ASGRKM8nX+eT3N74blOXWdlAJgHPV+FwTPbt7lDMPLkM7TMXIs4klK4o9HIOp2OtVotN4AAsHK57Ah2Pp9HwEI+vz9nVq1WrVQqRdCqWfRCcn0m9J08nIJEvodgBcdOlJME7IVR+3a772mq5/W0cl2FPcPzhdGGfg55RopPKLJg74cVoupYtHgjTBX8SLLZrPfqPT099QhUmRqMMetu9qbD5XLZisWi1ev1SLEX4wBYK7NCNMlYdDzKHoSgnb1cKpUcsCVxoM1m0/WJKJk1JQWBzrEmMGCkWcz2nX60RkQDHuyKpskoXmJ/MVbyr8p6MVcK5uOuI+vAHOtVj+iX2Vt7PvYFn4mD16OPrAdrGa5LWJiJ3jHP6ALAh7PuuVzOnp+f/dalf43C5cHowEK0ZmaR6ih+pg+/2Wy8iEKr2TQCPYRulIJC2cOJ4+90sdj0h3IWPxKegzyRWXRTMka9sFe/Ey2poiNK9WjVF7Si9vVUqkZfr9XKmltLkldCeI0WSCFKo4ebRY2NFnQpzXmoWlLnRClNIk+MB9Q5vyNaSkL9hYCt0Wh4PhInoF2g0EXmHoNIREFeRCNzdZ44+tlsZoVCwRt0aw5ZawQQjT4BQ0kcKA4QxmK9XkcqmvUZ9Vl4Zv0ZTIH2ooZC0wpF7S4VAs2wgAwDxf5gbZM4ULrNADLCvaf0Jv8GmFNVrVEY0Qj/Z+21y44evVLaN8xnKxVZKBT8ikMYqLjryDMqVTkYDPxzeF517IAXgD37R50MexN9VjZus9n4DVHMKftDHS9pJnQfejzJkaRsNmuNRsN1gJoW8tj6fARKMDr4lJOTk0i6EL3EfmreUtvGKrBjzkgxAATZ40dHR7ZcLq3b7Vqn07HBYPDv5kBRTM1Vmr0dT0Hx2HgoIAqHQ8MYcVOJTobmXnRDEPGGjcnz+fw3xx54LYqSlMIlEiT5rgUCZhZBeEQARBpsaqUlQYV6rkpBADkovlOdqdE576lOnDkOKeE4Y2Q9eT6ltBi70rXZbNbXgY2H0SbhTwQU5goxVIredZ51o/MsanTf0/kEpzKbzazb7XpRjxbMaDEFcwlFr/Sm5pvVsYdFLVBN0E1axKT0KtFEJrO/ro81TzJGzfWH5+XQLeaVCmOcHGvP+2CIlBZF1OnobR+hg+Z9NY2i+xkgrXvzZ5LL5ZxC1W5Qhw7Da/5QKWstEtFiLS3Y45kVjGqkEs4dewBHBdjC2ZdKpdgRaDabdWBycnLibegAlpq/UwDOnMJqhGyNRntm5s+prByOS22N5iQ1dYbNAayETNLPxlir1dx+me1PGaD7pOS05kXzwVodjB5o3YLWv2iAp9W92Du1cTAHpFD6/b7d3d3Z7e2tr8P3JJEDVeVSRIbi6VU0mlxnYTRPpBFLmHdTaoYBh3kmXWA1CCAnaFelJJKIRp2ABD5HKw5R6tDIo5gaNeszqAEJc4FKgWmUgBMLK1Q1wogjOEulv3hvM/MCKdaWjcMcs7G5jUWdqBpf1pR8Is8ZAiV1nrvdzlFhGDkldaC0CRwMBtbv9+3q6soNMdEnBlWrDZfLpRUKBe/BySaez+eRAiMFbkTKgApy/UTU6IMa4kKhYLVazWq1mpf4J7kiSgsszPa341QqFd8rzJuCGS1e0mhbu2bp++vn8KXUJ/oTsiC6R1kTTR3EHaOukVKJGkkpcFO7sl7vL86myj1M/egeYw2xOcydzosCTy2Q09aPFKIkGSNOdDab2XA49LSGOkH2LWMkutI9pMGN6oeCWOYQW44N10hdaXv+HjsB9ZoECFWrVTs+PnYHPxgM7OnpyXtO85wh+6j3hIY0PD0FqLFQlgHGgoIjgjVlPQGPBC7Pz8/W7Xbt69evdn9/70fdvifvrsJVOhHjyOFTrfBkcZgUNSKK7vgbDLpu2rCaTzekPptuhO126537k+RcdHNo9SDREg4ZukerSkNePSykwUCj3GoY+DcAQtE0kR9GV8/QKoJO4kCpTAtzX4wPOpP5VsTKhlbDTETNnOl6sWFxnKw3RlgLI9RQKtJ+T6EUDnAymdhkMnHnhLEiCoXyhEZGiCypVNQ2dKFDR9cxwHqMiVw8kTy6fXp6apeXl54bwkknWUctGHp5ebHJZOJX5IHElToHiDGn7C+QvEZnqsPMqRp0xqaORo0wNL3qjVKQcdfRbL+HcR5aX8CX5ll5Fl6jzpJxaF46TDUoyEEf9Tn4O5wKVL8em0gyRtbl48eP1mw2rdVq+TE6CmHM9vUDqqf67GFKDNH8Lc/H8+vpAnVA6AGRO/MMCEvC7EHFLxYL7/TF+Wp+xnMxd1oohu4AKlhXxs0z63Vu2CwNAFhzBfqkJrLZrM3nc+t2u/bw8GDtdvunwP1dDlQRgtk+5OYhNFJlk4W5I17PhgypGI1i+K6bGgmjNM4QaSSTRJnVMPC5Si8w3t1u57SsVhzznFpZqxtb31MNlDolKGKcpAINTf7ruNSBxxE1CiDvEG0z5kLhrWEGCs56KxWt9Arro7loPlM3NnPNPCoLcQgkmSUrsMH40B+UYjbQK7c5zGYzr0CkAlhBHHOkZxl/JCEwBOVqD9IPHz5YvV638/NzK5fLNh6PvfIvrgPFcGu3Kho/aCpAgS9fGBmMJN/13+FeYx7MLGK89CgS49azeWYW0W11ynHWUQ2odugJHRlzH+Z9w2iVPRQ+O++BzqrD0ahMQQO5NMCY1mTEHSM5wUql4vnlarXqDST4LLWhmhJQ5x46V3RYHaE6VgW5vF5BlF4Jx74w2wPtuPuR51MnbWbOZnFJvdLqCuyxDYBFXgtbQBCiPkUZLl1rdcR6W896vfYbXAaDgXW73Uigd0jeVYWL4ii1CgUAlcsDfu8B1OmpkuuChPSRWfTsjkaLbAoMZjb71qBZ0XccWa/Xfm2aohsMkVJYGATNEzIXIHoteVfHabbPKZO/gtqgDyb5D1UejeBQLhxg3CIbDG8mk4m0SOPziAJDQ6t5AzadInYcariOivRVwfXA9Gaz8Y5VOFnel42XtJoaWpZD1zqfHHafz+euM8qc6DqzOTGQ6hh1LfVaJOYCfcUYwTSUy2VrNptO9e12O5tMJtbtdmNHabncWw9Vcq8Ar9FoZM1m08rlcqQQLqwTOLRG/PuQ82ScFM+EN3RopK3nngHUpHj4WRwhZaLt3aDYlRniudWZopM6XuyWpog0KtW9dmj/KujjmcJ0EjYhLhBar9c2HA69mEwBHseu9BiYjlsra0Mgrukk7KfqQBitEnGjpzQV4CwlNob5S5LL3mw2fgxJTx5Ar1L/oRG2Bmp8VsgAKOvBGmMreL1WGlOXwGs0RYc9ovhoPp//uw50t9v55asUDaF00Ljb7daRfrhQYZSEMmouQeleVeaQ/lKEwqKSe3p6erJisRg5EhFX1uu3c0oUOtErlShSaUvQkxpculmEOUpdZN5DDZG2rmIBeW+OVdC1SJFyJpPxfGTcDZvL7buUEBHBFnDujPyYOjEUDkemFcOHDLNSfvweQ63RBMaBL5QaQ65RXFzBubAhiDK1yQUXhONEcQK0p0PvqOTEIWkqQQ3TYrGIHEnSaEHPlp6enlqr1bJqteq/f35+tsFgYA8PD7EdaLFYtLOzM3t5ebFut+sAYTgc2nw+t0aj4Q7UbG9ItTkE30O6L3SuiK6hVqwSIRGNaaSjnbqYuyQOFGDMOdOwEE+NJYY1zIuq3UA/cByh7qLj6jwBlABe2ArmR6lGbGDc/bhcLu329jZSiKTNNThvHq5POIehfdQgBbsaph3CegWiVI56aXEN9Q5U0FYqldjs3mq1ssfHRwfi2PPVauVNTBqNhoNU5prnVLpcPxNdxIZpThgbS6MIKGNsKuuvR3vUVoXR/CFJXEREjoZzZgyKhSaqyefzTqWqEWUBNQqBwgUhKnJS+jc04Lw3kzSbzbzjCIqgR0riyGbz1sGGiIjkOQulFW6a4FYAAKeuraQU7WieE/ROno22Y2xSIvxyuRwBI0SFmUzGXxOXMsKB7nY7Pz7Bs7Amethaq/lwBiHlzoZVNI+oDuA8NdJer9d+cFrz4eRNyVPGjbDN3pzL+fm5l6FTYDObzXxty+Wyz3NY8q/OG8oaEKPnzZgDKMHwXK+OA6PYaDSs1Wo5iFkulzYcDu329tZubm5ij7NYLNr19bVNJhPb7XYOEEqlko3HY6eHwwKhbDYbAQwU2oRAKGSQQmAE66OpHM0pY5QAS1qsFndPMrdUNlPlnM2+VXXqXa2a0zs0FsYAkA3HhOi6a3oGpod9SlHSZhO9c1LPAMeR5XJpnz59MjNzwHOoLiJk55TBU30EdGCnzL6trOXvmCMFDaVSySlkGjNwNGY6ndp4PP7GGf9M1uu13d/fW7VadaoWMDcajSyXy9n5+bldXFxELqzHvmB/1HmqzdFolfXXyniCEmX0cJ56pjmXy/k+Pz09tdVqZfP5/LvjSkzhkhtCYaBl1FEw0drZgkXUgSotqfmvyAMG5fN0AyHXAP05nU79zB+XwRKBKJf+M1mtVk6j0cMXg0GUC42klahqFELKT6lAEK9udhZaj7rgvFhQ5s9sXz2JwdduRXEkm3071IzjxPiAollf6FyOdWA8aAXGOLQyWJ8hzIWa7SuFQ6OqEVpYLMZ7JwEJxWLRfv/9d8vlct75SqtxqZhU545jJw1hZhHHjzPQsSm4Yv306AoGG304OTmxZrPp51JxZvf393Zzc2OPj4+xHWihULDLy0t7fHz0fTeZTOzo6MiGw6FNp1NrtVq+Z9SI6piVClOQq+kaBQRhdGO2d54atelnqE7z3nEEZ8B5xeFwaKPRyHa7nV1cXHi3KCqOFcyY7UE4a8YeUt0MI+zQwfC+6D/GGAYOXWZ8NHWP60BfX1/t06dPHpiYmVO5/J+ISnOPmvoKixb5QnCQYQQHbcvvS6WS66e2waOvcL/ft9lsZqVSKTKPP5PVamXD4dDPbCol/vT0ZJlMxvr9vk2nU6vVag7smR8FAyFY327frlvTlB/rBeCitgE2j9xurVazSqXiugBD1Gg0zMxsNptZv9//7rgSt/Lj4TT6ouExhhVUMR6Pv6maU7pFCxo08tBFwcnqHY3Qjjie8XhsvV7P2u22F2NQzaYGIo68vr7a7e2tvby8WKvVslqt5s+ntKtWZx66pkrHEiosmxIErwe4dTNrVdnHjx8jERJUI0oU5h1/JLlczs9Ebrdbp4ygZhjrfD53h4YDVXoOY6VUnhognQetzDXb09iZTCbS7hDUTcSH4SUfEZcy+vDhg/3xxx9mZnZ/f++Grd1u26+//mq1Ws2bGBA1wGIQnRFxKIUHvYvuolcACdWH1WrfLYWjDWxOutW8vLzY/f29ff782Tqdjk2n09jOJZ/P2/n5uZ2dnVm1WrV8Pm9PT0/W6XTs/v7ezs7OvMoXXdKimGw26yAXZ4/DV71S0Kt5UhwtDQQ4phBWeWrhhjrrOMKcM6fT6dQN2vX1tZmZswlKn+peUGozrOLnOZQ5UQpUwTOpAG1UgE5yhnY2m9lkMrGvX7/GdqCr1cr+/vtve3199ejs4uIiouvKkKg90rQYeVelPBk/tRxaEKWRNjpK16fj4+NIYU2v17OHhwc/XkMPZY18fzbGfr/vFeLKzq1WK5tOp9btdq3X63l6g0CBNExYM6PHyNiHCi5gCsh7sgfYg1z6QKDF0ZdGo+E3vBwdHdnnz5+/O65EDlSLT1BsemFC+9HJoVKpeLs+pTj1WIhZ9MorlFuVPYxAMd4oFIUXd3d31uv1vIdkpVLxKCLuZmWhv3z54mchr6+vfdyKEMPIBCOsRUsYCzajVi5qRKOKwHyweDiekI7SiFdp7bjrSAT6/PzsXV44t4hAd2iUydlXjT4PtQ5T46tNL9R4o9C00MKJanOJ5XJp4/HY5yDuGIvFov3555/+2Z1Ox15fXz2CaTQakbzPycmJVSoVq9frfvwEsMRaAyBwMJpuAFxpXhdwAIXKWOv1uqPewWBgX758sbu7Oz8XFxfsZTIZq9frdnl56YZgvV7bYDCw29tba7Vadn19befn55HbRLTwSUEAqF7XHzn0d+xRzvHp+vEa1RON8OPuye126wCNYpDRaGSvr692fn5uv/76q9N+OG69yksNqx5DOpQnDceI7mOMtTc1gYHSizAd/X7fvn79Grt383q9tsfHR3t9ffWORIvFwmq1mkdN2WzWGY7tdutjIerVPG9IX5vZN4Vb2GEoTEAIYNrsLZiA2Wu329br9RzgEb3FdaCvr692c3PjrQ5xYNy9ix3vdDp2fX3tNxmpzVcwpvZT11jnlN8TwGlut1Kp+DPgT6ibqFarzhgNh8MI5R9KIgeay+X87spMJuPIAUeZy7015MWBlUolR7goEwhBN3LYHUN/pp32MV7kPMfjsXW7XWu32/b4+GjdbteNLfSk0kxxZLvdWrvddlQJEqEfKsnoQyhWUbdSe2x+qD2lv7QSEIMECg3pNj5Pi5B03pI4UA4gc/1Wo9FwIARyxrmoIaHCUAugiC60aEodKNQs0SuREMAEw8sG5qtQKFi/34/QoHGlUCjYX3/95cVg2WzW9bTX63n0h1OheKPVavk6QS9hNPXIhxoqjBXzwKbW/ApjhTrO5XI2GAzs7u7Out2u9ft9B5px19HsLfriOMzZ2ZmdnJxYr9dzJ3p1dWUXFxe+H4nUwkpKCnTQ5TB3qDoegiNlD9irsBPoqfZ1DY37jwTgwjxrJe7t7a399ttvdnl5abnc26XUxWLRP4vLqYkSAUwI9RX8O8zbMx/adUujdf5uu906e2NmHq3FLQbbbrc2Go1suVxaqVTyFMovv/ziwIBcKExJNpt1m4QtORRNs2YwD2bRoIXAhCYOxWLR2afn52cHnPQvXy6X7oSS3EG8Wq3s7u7Ojo6O3HGy3zqdjk0mExuNRm7Dl8ulF+2FN1lpnllte1hERZEk4/348aPndQHMMHvkPOv1upntKfTw2E8o73KgSsMsFgu/KxEF4OGq1WqkzRuUFqLnjbTQAYriw4cPjmi1MhOKuNPpWLvdtm636+hlPp9boVCws7Mzd/JqGH4mmczbNTaDwcDq9bpTwoy9VqvZZDL55rwSC8nza26Fz9c826FojaizXC57scr38sOgIlpaxTVIjBGwAxqr1Wo2HA5tsVhEnp0IAzDA+uFUQ9Cg1BfzoRQ6Y4GWpwclkRnHL2jzyHt971jF9ySfz9vV1ZUXQ8EOZLNZm06n9vj4aIvFwprNpqNQIsRGo+FFIgp4NBeI6HhDMKSvYzPTZ3Q4HHrOk1QHhi4uqmd+S6WS1et1u7i4sFar5RR0r9ezf/75x5vpYwz0uieelYpzZUNYKz2ChG7DIOBAQ51Fx8ldzudz34thmuZHstlsvK8wlKPZvlr+4eHBrq6u7PLy0qrVqjenwOlSo6F7lc/G2KpOa34N56mtOjUPp/UCdKnabrfW6/Ws0+kkAu7kGdvtdiSyPDs78/2ohYesE2BMn11rETQ9hp3lS0GtVhmzZuPx2O82Ho/HXi9Rr9cjvZDjrmOn0/HuW1S1t1ota7VaDiD7/b71ej0//6oMFnlLxhYWsbEuWvjH6RACIpgYdJWfV6tVtwXoAlT9v+ZAM5mMc/2ctTQzp9nG47FTVuVy2R0oD6JFI1rdRqSjhQ46AZQ1QxeysKCj8XjsnWYw8mHFa1wHymuhiobDofX7fbu8vHQjgcHXAiEWCYfB4qP8aoTMooftQYM4FV1cDB0KG1KgGNwkkQsKiHNkI1WrVUfumm9BiTG02exb+bl2DQrbnzF+PVemaJd5JOdSr9ft7OzMGo2GVz5rzjd89jjrSOXycDi0Vqvl1yjlcjmP9jBKnBmmirpcLjt7ovk+niEsuDHbF0hptatZtFADqg8HNxgM7OXlxecpn8/bYDCINUb0Kpd76xdLzpO7M2mKfXNzY81m08/18YwYUeaYc70YaDW8GtHw2rA2QelRIlC9gxMgpSmcnwn0qRbUwQxtt1vP+Q4GAweCyiSEwE5TLLqO/CysLlfKEJ1WMIyTJce2Xq9tNBolymWzT6j47Pf7DpwXi4WVSiV34GpHyPUy99r4RHOl2Ncw/8k4cULkSWEWe72e9ft9L5DiM7jyizmMu47j8dhKpZIf17q8vLRisehXDvI84/HYhsNh5NgYdsPM3JZg38NaEPaSnptX2wotDLXbarU8BYIDfXp6skqlYr1e74fjyiSMXHpmdhP7Bf8t+W2327V+9kfpGP/zko7xf5KO8T8v6Rj/J/9fx5jIgaaSSiqppJJKKm+S7IqSVFJJJZVUUknFzFIHmkoqqaSSSirvktSBppJKKqmkkso7JHWgqaSSSiqppPIOSR1oKqmkkkoqqbxDUgeaSiqppJJKKu+Q1IGmkkoqqaSSyjskdaCppJJKKqmk8g5JHWgqqaSSSiqpvEP+D9lmVaRcnz/xAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x288 with 24 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3,8,figsize=(8,4),subplot_kw = {\"xticks\":[],\"yticks\":[]})\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    ax.imshow(v[i,:].reshape(62,47),cmap=\"gray\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_pca = pca.transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1348, 150)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 将v与原始数据x相乘得到降维后的数据\n",
    "x_pca.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1348, 2914)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 无法对数据完全逆转，只是把降维后的数据转换到原空间\n",
    "x_inverse = pca.inverse_transform(x_pca)\n",
    "x_inverse.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(2,10,\n",
    "                         figsize=(10,2.5),\n",
    "                         subplot_kw = {\"xticks\":[],\"yticks\":[]})\n",
    "\n",
    "for i in range(10):\n",
    "    ax[0,i].imshow(faces.images[i,:,:],cmap=\"binary_r\")\n",
    "    ax[1,i].imshow(x_inverse[i].reshape(62,47), cmap=\"binary_r\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 噪音过滤"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "digits = load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(4,10,figsize=(10,4)\n",
    "                             ,subplot_kw = {\"xticks\":[],\"yticks\":[]}\n",
    "                            )\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8,8),cmap=\"binary\")\n",
    "        \n",
    "plot_digits(digits.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为数据添加噪音"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.RandomState(42)\n",
    "\n",
    "noisy = np.random.normal(digits.data, 2)\n",
    "plot_digits(noisy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "数据降维"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 6)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(0.5).fit(noisy)\n",
    "x_dr = pca.transform(noisy)\n",
    "x_dr.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "逆转噪声数据结果实现降噪"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "without_noise = pca.inverse_transform(x_dr)\n",
    "plot_digits(without_noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
